Surface area and volume of 3d shapes formula sheet Here, the base is a rectangle with length 12 cm and width Get your free volume formula worksheet of 20+ volume questions and answers. Volume formulas can be easily confused with each other and with formulas for calculating the surface area Find and save ideas about area and volume formulas on Pinterest. 1) Find the volume of the cuboid given below. Curved Surface Area: CSA: m 2 or cm 2: If there’s a curved surface, then the total area is called a Curved Surface area. 9 cm². The area of all the surfaces of a 3-D shape. Surface Area and Volume of 3D Mensuration is a branch of mathematics that deals with the study of different geometrical shapes, their perimeter, area , surface area, curved surface area, volume etc. The opposite faces of a rectangular prism are congruent. Surface Area Of 3d Shapes. Here are the essential formulas: 1. Pyramids The surface area of a 3D shape is the total area of all its faces. Please, also, check out my other resource: (Formula Sheet) ‘Cool Volume and Surface Area of 3D Shapes 731316 worksheets by mutiyah . 2 i n 2 in 3 in V = 12 in³ SA = 32 in² Grade 6 Geometry Worksheet - Volume & Surface Area and Volume. Pinterest. The volume of a 3D shape is the amount of space there is inside the shape. All the required formulas of area and Algebra Formulas Slope of a Line 21 21 rise run yy m xx where xy 11, and xy 22, are points on the line Linear Equation: Slope Intercept Form y mx b , where m is the slope and b is the y Solutions for the assessment Surface Area and Volume of 3D shapes - advanced 1) Volume = 216 cm 3, Surface area = 216 cm 2 2) Volume = 200 cm 3, Surface area = 210 cm 2 3) Volume = Surface Area. Its examples are cubes, spheres, and pyramids. g. A Perimeter, Area, Volume, and Surface Area For problems 1 – 4, match each question to its answer. Reiterate the concept of surface areas with these printable Find the surface area of the following cylinder: Step 1: Find the area of the two circular faces using the formula for the area of a circle. This document provides formulas for calculating the volume and surface area of various 3D shapes. surface area of 3d shapes . The surface area of any given object is the area or region occupied by the surface of the object. Your Favourite Cheat Sheets; Your Messages; Your Badges; Your Friends; Your Comments; Math Formulas Geometric Figure Surface Area Volume Cylinder r h = A 2 base = ˜ r A lateral surface 2 ˜ rh A total = 2 A base + lateral surface = 2˜ r 2 + 2˜ rh V V = (A base)(height) = ˜ r 2h Sphere r A = 4˜ r 2 Transform your youngster into a math champ with lots of intensive and informed practice, and let them surprise you by solving problems on surface area twice as skillfully. 5 i n 4 in 2. Volume is the amount of space available in an object. docx - Free download as Word Doc (. Surface area is You are here: Home → Online resources → Geometry → Volume & surface area Volume and surface area: online games and resources. The lateral area of the triangular prism is the sum of the areas of the lateral faces; i. 5 cm)² SA = 4π(12. Volume and Surface Area of 3D Shapes worksheet LiveWorksheets LiveWorksheets transforms your E4. The surface area of the prism is the area of its net. It is measured in square units (e. Log in. 4 i n 3 in 4. May 19, 2022, 16:45 IST. If the cost of the painting cylindrical tank is $6 per yd 2, what will be the Surface Area and Volume Worksheets. 2 Substitute known values into the 2D & 3D Shapes differentiation with Perimeter, Area, Surface Area, and Volume formula. Check Details Surface area of 3d shapes • The surface area of a 3D shape is the total area of all its faces. Calculate the volume of the cylinder below. There is a worksheet that can be used in a few different ways, it can be given mostly blank for students to fill in, cut out and used as a matching activity or given as a complete sheet for revision. Volume = 4⁄3πr3. It is the total capacity of any object. Surface Area and Volume Handout These Surface Area and Volume Handouts has useful definitions, facts, and formulas for cubes, rectangular prisms, general prisms, cylinders, Surface Area worksheets for Grade 8 are an essential tool for teachers to help their students master the concepts of geometry and area in math. 2) Find the volume of the cube given below. A cube or a cuboid, has six faces. Composing Shapes. 5 i n 5 in Grade 6 Geometry Worksheet - Use this teacher-made Maths formula sheet pack as a handy reference when your students are prepping for exams and memorising different formulas. 1. 3D shapes are measured in two terms that are: Surface Area-The area of all the faces of a solid is called the surface area of the object. Enhance your math skills and understanding with this visual aid. The surface area of a 3D shape is a measure of how much area the surfaces of that shape have in total. Find the height of the cylinder. This worksheet will show you how to work out different types of surface area of 3D shapes questions. 25 cm²) SA = 4(12. It Explore printable Surface Area worksheets for 7th Grade Surface Area worksheets for Grade 7 are an essential resource for teachers looking to enhance their students' understanding of Let’s explore the various 3D shapes you are likely to encounter and explain how to calculate their surface area and volume. Question Paper. 3. Platonic Solids 3D; Euler's formula for polyhedra; Sections of Triangular Prisms; Cross Geometry Reference Sheet – 3D Shapes A Sphere. surface area of rectangular prisms Area shapes surface formulas volume math 3d formula geometry circumference geometric sheet organizer figures 2d perimeter foldable chart graphic mathsSurface area For calculations, Lateral Surface Area means curved surface area. The surface These worksheets provide a variety of engaging and challenging activities that help students explore the properties of three-dimensional shapes, such as surface area, volume, and cross A 3D solid refers to a closed, three-dimensional shape. This Surface Area and Volume Worksheet will produce problems for calculating volume for prisms, pyramids, cylinders, and cones. There are a range of different 3d nets to find the surface area of including cubes, cuboids, prisms and This chapter dives into calculating the surface area and volume of various 3D shapes. In Geometry, a Surface area and volume of rectangular prism word problems worksheet; TRINAGULAR PRISM. As we transition into the realm of three-dimensional (3D) shapes, mensuration takes on new An interactive activity that tests students' ability to work out the surface area and volume of a cuboid, triangular prism and a cylinder. Name Surface Area Lateral Area Volume Right Prism S=2B+Ph L=Ph This should allow students to learn them more easily: students could pin the poster on their wall at home so that they can view the formulas every day. Topic: Area, Solids or 3D Shapes, Surface, Volume. Surface Area Meaning \(S A=2 B+P h\) Find the area of each face. The heights of the Shapes volume area surface 3d formula sheet cool geometry teaching prism maths math solid tes board resources practice trigonometry mathematicsShapes prism dimensional Surface Area worksheets for Year 8 are an essential tool for teachers to help their students master the concepts of geometry and area in math. Lateral Area =+ + =++=3 6 4 6 5 6 18 24 30 72() ()( ) cm2 Feb 4, 2021 - Surface Area and Volume of some 3D shapes. Some important ones along with their real-life examples are listed in the section below: 1. Feb 4, 2021 - Surface Area and Volume of some 3D shapes. Pyramids Detailed Description for All Volume Worksheets. Further Maths; GCSE Revision; Revision Cards; Books; Basic Formulas For Volume Of 3D shapes. com Created Date: 20201229113226Z Surface area = 2 × 20 + 60 = 100cm2 Surface Area = ba + la Example: ba = base area = 16cm2 la = lateral area (all sides) = 60cm2 Surface area = 16 + 60 = 76cm2 Surface Area = fa × s 296118445-Geometry-Formula-Sheet. Symmetry. Mathematics. They are drawn in 2-D space and are dependent on 2 parameters, generally length(l) and breadth(b). Surface Area Formula . The volume of a pyramid is one third of the area of the base times by the The formula for the surface area of a sphere is A = 4πr 2 and the formula for the volume of the sphere is V = ⁴⁄₃πr 3. About Surface Area and Volume. 2. Copy and Edit. The surface area of a 3D shape is the total area of all its faces. _____ 10) Find the volume. Volume of the cuboid = Base Area x Height. The 3D shape is a cylinder. Volume of a pyramid = 1 3 1 Write out the formula for the volume of a triangular prism. Bud [FREE] 3D Shape Worksheet (Grade 1, 5 and 6) You can find the volume and surface area of 3D shapes. The formula you need to use is \text{Volume}=\pi How do I find the volume of pyramids and cones? In a right-pyramid the apex (the joining point of the triangular faces) is vertically above the centre of the base. The volume of a 3D shape is the space inside it. ) Find the volume Cheat sheet for area/volume/surface area formula for 2D + 3D shapes Volume and surface area of cuboids and prisms. Images are included to SURFACE AREA AND VOLUME OF 3D SHAPES CUBE. Volume of prisms including cuboids This cuboid contains 12 small cubes. Answer-The surface area and volume chart will make it easy for students to compare the surface areas and volume formulas for many Surface Area and Volume of 3D shapes. Shapes that you have to work out the surface area of can fall into one Volume and surface area formulas posters set, geometry, 3d shapesVolume and surface area formulas posters set geometry 3d Shapes area formulas formula different 3d math maths Solutions for the assessment Surface Area and Volume of 3D shapes - advanced 1) Volume = 216 cm 3, Surface area = 216 cm 2 2) Volume = 200 cm 3, Surface area = 210 cm 2 3) Volume = It provides formulas for finding the volume of prisms and cylinders by multiplying the area of the base by the height. Area and circumference of circles. Geometry cheat sheet2d / 3d area / volume/ sfa cheat formula sheet Surface area of a cone formula explainedFormula for 3d shapes. e. Formula to find the total surface area (that includes the base or bases according to the solid). Area of a circle =πr 2 Area of a triangle = 1 2 bh Area of a parallelogram =bh Example 1 Calculate the Surface Area and Volume. Volume 3D Shapes. Submit Search. Find the total surface area and volume of the following, correct to 2 decimal digits: 2. It's called lateral surface area for cube and cuboid and curved surface area for cylinder, cone and 3d shapes area and volume formulas. 91 in³ SA = 209 in² Grade 6 Geometry Worksheet - Volume & These surface area and volume formula sheets challenge students to measure various prisms and extend to interpreting complex worded problems. Surface Area Formula includes formulas for 3D shapes such as Cube, Cuboid, Cone, 2. A prism is a geometric shape consisting of a stack of identical base shapes stacked on top of each other to a depth d. These worksheets provide a variety of The surface area is the total area that the surface of an object occupies. 3 i n 3 in 2 in 3. Volume of any object is defined as the total space occupied by any object. Show Menu. Level IGCSE Subject Maths (0580) Exam Board Cambridge International Examinations (CIE) Level Core Topic E4. The surface area is the total area that covers a 3D shape. docx), PDF File (. Volume surface area formula sheet Area of shapes formula sheet Shapes area formula 2d sheet geometry Volumes and Surface Areas through Mensuration in Maths in 3D Realm. . Worksheet . The volume of the cuboid is 12 cm 3. The lengths are to be chosen and entered. Surface area is defined as the total area of all surfaces VOLUME OF 3D SHAPES WORKSHEET. 4th - 9th Volume Formulas – FAQs Define the Volume of 3D Shapes. 7 i n 7 in 4 in V = 196 in³ SA = 210 in² Grade 6 Geometry Worksheet - Volume & 9) The volume of a cylinder is approximately 5626. use appropriate formulae to calculate the surface area, volume and capacity of a cube 2. This prism is a This document provides formulas for calculating the volume and surface area of various 3D shapes: cubes, cuboids, spheres, cylinders, cones, square pyramids, and general pyramids. See It also describes how to calculate the curved surface area of a cone by dividing a paper model into small triangles and summing their areas, which equals 1/2*πrL. Total Surface Area (TSA) of Cylinder = 2πr 2 + 2πrh = 2πr(r+h). Add up all areas. What are the Applications of Geometry Formulas? Geometry formulas are useful to find the perimeter, area, volume, Concept: The surface area of a shape is the sum of the areas of all its faces. A series three-dimensional geometric shapes is shown in text form or as a drawing in a table. Today. Cube. pbrucemaths. Basic Formulas For Volume Of 3D shapes. Surface Area (SA): SA = 6a² (where a is the side length of the cube) lateral surface area + 2 (area of the Base) area of the Base x height: Circle Cylinder: area of the lateral space (rectangle) lateral surface area + 2 (area of the Base) area of the Base x height Curved Surface Area (CSA) of Cylinder = 2πrh. It defines key 3D shape elements such as faces, edges, and vertices. The table provided depicts the formulas to help in calculating the surface area Formula Sheet Grade 9 Academic Triangle Trapezoid Parallelogram Circle Rectangle Geometric Figure Perimeter Area w l A = 2 bh A = 2bh 1 A = 2 (a + b)h 1 d r h b c b cd a h 2 (a + b)h A PPT aimed at GCSE foundation - covering area of rectangles, triangles, parallelograms, trapezia. Mensuration Formula of 3D Shapes is discussed below in this article. The surface area of a 3D shape is the total area of all the faces. 7th - 8th grade. Where: r is the Radius of the base of the Cylinder; H is the A reminder, a face is the surface of a shape. Surface Area (with top and bottom): SA 6= s2 Volume: V 1 2 3 = πrh Surface Area: SA 4= πr2 Volume: V 4 3 3 = πr Rectangular Solids (Boxes) Cubes . What is perimeter? A. This document provides formulas for calculating the volume and surface area of various 3D Here is my comprehensive 2D and 3D Formula Sheet for area and perimeter (2D) and volume and surface area (3D). These worksheets provide a variety of 1) Find the volume and surface area ofthe entire cone (with radius r). illustrating the surface area formulas This easy-to-use toolkit packed with pdf worksheets for 8th grade and high school students, to determine the volume of mixed shapes covers a great spectrum of exercises involving a variety of 3D shapes like: prisms and cylinders, cones IGCSE Mensuration Formula - Free download as Word Doc (. 6 i n 7 in V = 230. Geometry Formulas Foldable Volume Surface Area Perimeter Circumference Graphic OrganizerThis is a single page PDF foldable that can be used a reference sheet/study guide Mensuration Formulas for 3D Shapes. Author: Jason Wofsey. 4. The sum of all the areas of 3d shape is called _____ area. Volume and surface area worksheets are essential tools for teachers who want to help their students master the concepts 0 result images of 3d shapes worksheets for grade 3 pdfVolume formulas for 3d shapes Shapes volume area surface 3d formula sheet cool geometry teaching prism maths Volume & surface area of 3D shapes Grade 6 Geometry Worksheet Find the volume and surface area. • Volume of a pyramid = 1 3 1 Write out the formula for the volume of a triangular prism. 47 discussion, as there Surface area worksheets comprise an enormous collection of exercises on different solid figures. The sphere is a 3-dimensional (3D) object, whose surface is continuous and all points of the surface are an equal distance from a fixed point, the center. This is an annotated and hand-picked list of online games, worksheets, activities, and tutorials related Surface Area worksheets are an essential tool for teachers looking to enhance their students' understanding of Math and Geometry concepts, particularly in the area of three Download Formulas for Perimeter, Area, Surface, Volume Cheat Sheet and more Geometry Cheat Sheet in PDF only on Docsity! FORMULAS FOR PERIMETER, AREA, SURFACE, VOLUME Edited by J. Each small cube has a volume of 1 cm 3. What is area? 9. p 4 Find the curved surface area of the cylinder correct to 1 decimal Surface Areas and Volumes Formula: The surface area formula serves as a mathematical tool to determine the cumulative area covered by all surfaces of a three-dimensional object. doc / . 4 3D Shapes: Volumes & Surface Areas. The basic concept behind Surface area and volume is that it is calculated for any three-dimensional geometrical shape. In the past students have found the volume of the shapes, surface area the shapes, h. Find other quizzes for Mathematics and more on Quizizz for free! Worksheet Save Share. First, we must write the volume in terms of x. 4 cmthe area of the circular ends (iii)the surface area Give the answers correct to 2 d. Formula to find the curved surface area or for the lateral surface area. 1. The volume of different 3D shapes can be calculated using different formulas for each shape. 2 Substitute known values into the Learning the formulas for volume and surface area of 3D figures can be challenging when learning about more than one figure. Lateral Two different measures are used to measure 3D shapes: Surface Area; Volume; Surface Area is the total area of the surface of a two-dimensional object. Solve real-world and mathematical problems Formula Sheet area of a circle = ∏r2 volume of any shape = BASE AREA X HEIGHT (or length) volume of a sphere = volume of any shape turned into a pyramid = regular volume This document provides formulas for calculating the volume and surface area of various 3D shapes: cubes, cuboids, spheres, cylinders, cones, square pyramids, and general pyramids. With this single Geometry reference sheet, students have quick and easy access to the formulas they need to solve any SURFACE AREA: The formula for the surface area of a sphere is: SA =4πr² SA = 4π(3. Intro to Solid Figures. Understanding how to use the correct formula for each face, such as a triangle or rectangle, is AREA AND VOLUME FORMULAS Areas of Plane Figures Square Rectangle Parallelogram • h A = πr (π ≈ 3. The triangular Title: Math Formulas For Surface Area Of 3D Shapes Cheat Sheet by Cheat - Cheatography. SUMMARY OF THE Print on A3 and let students work out what they can. A hemisphere and cone are joined. The surface area of a 3D Videos and Worksheets; Primary; 5-a-day. In the net below, the Learn essential geometric formulas for volume and surface area with this informative anchor chart. This may seem a little different, but it actually comes up a lot. Spheres . It includes formulas for calculating the perimeter and area of rectangles, squares, triangles, and circles. Surface Area And Volume Formula Sheet Geometric Shape Perimeter Area Circle d r C = πd or C = 2πr A = πr2 Parallelogram h b c P = b + b + c + c or P = 2(b + c) A = bh Rectangle l w A = or A = bh The space occupied by a 3D shape is called a Volume. Step 2: Find the area of the curved face in the middle by VOLUME and SURFACE AREA formulas posters set, Geometry, 3D Shapes, Educational posters, Classroom Wall Art, printable, digital download This set of 8 posters is a great Calculate the curved surface area of the cone using the formula, Calculate the curved surface area of a hemisphere using the formula for the curved surface area of a The graphic on this page, is designed to be a quick reference for calculating the area, surface area and volume of common shapes. Shapes that have only two dimensions are called the 2-D shapes. - Download as a PDF or view online for free. pdf), Text File (. 2: Surface Area formulas; Geometric Figure . Geometry sheet eewebArea shapes surface formulas volume math 3d formula geometry circumference geometric sheet organizer 3) Find the surface area of the triangular prism 4 cm 12 cm 5 cm 5 cm 5 cm [1] 4) Find the surface area of the cylinder, rounding your answer to 3 significant figures 3 cm 6 cm [1] 5) A cube has With this great Volume of Compound 3D shapes Worksheet, students will get plenty of practice finding the volume of compound shapes made from cuboids, prisms, and cylinders. Upscale practice with an enormous collection of printable worksheets on finding the volume of solid shapes like prisms, cylinders, cones, pyramids and revision exercises to revisit concepts with ease. Show all work. , cm Example 1: volume of a cylinder. Gutt-Lehr Shapes Formulas Formulas for the perimeter and area of two-dimensional shapes, as well as formulas for the surface area and volume of three-dimensional shapes, are provided. Watch. Example: is a circle, S is the surface area of the object, L is the lateral area of the object, and V is the volume of the object. It gives the specific formulas for finding the volume and Volume of a prism = cross-sectional area × length. These formula posters will help your students learn this math This document provides formulas for calculating geometric properties of various 2D and 3D shapes. Teachers Pay Teachers Store Check Out identify a range of 3d shapes, and know how many faces, edges and vertices they have; know the common formulas for 2d shapes; know the formulas for working out the surface areas Surface area = 4πr2. $ # "## The volume of a sphere is the same as the volume of 2 cones (with the same diameters) 3D Volume of Mixed Shapes. The triangular Volume of a prism = cross-sectional area × length. We can work out the volume and surface area of 3D shapes. For more information and examples of these calculations Volume of 3D Shapes 723960 worksheets by mutiyah . Write down the formula. Find the volume of the cube if its edge measures 4√4 units. Shape Patterns. Perfect for math students and enthusiasts. The answers are provided in GRADE 11 SURFACE AREA AND VOLUME 1. Cube is a solid 3D figure, which has 6 square Area Formulas of 2D Shapes. Get Connected Math in Demand with Please don’t forget to rate me. Surface area Surface area of 3d shapes formulas Formula for 3d shapes Cube surface area formula Surface Area Of 3d Shapes Formula Sheet. It also Here is my comprehensive 2D and 3D Formula Sheet for area and perimeter (2D) and volume and surface area (3D). Examples Description. The base can The total surface area is the area of all the faces of the shape while the curved surface area includes the area of the side faces of the shapes only. txt) or read online for free. use appropriate formulae to calculate the surface area, volume and capacity of rectangular same throughout the shape, so we cannot use the formula area of a circle ×depth. 25)π cm² SA = 49π cm² OR SA≈ 153. Cylinders . 14 or ) Circumference: C = 2πr = πd Volumes of Solid Figures Cube Rectangular Shapes area formulas formula different 3d math maths types mathematical shape 2d find basic surface square form create standard lesson Geometry cheat sheet Geometry Here you will find our Surface Area Worksheet 6th grade collection. 9 ft3 with a diameter of 32 ft. Volume of a pyramid = 1 × area of base × vertical height. 13 Oct 2024 by Prof. Volume & surface area of 3D shapes Grade 6 Geometry Worksheet Find the volume and surface area. 5 cm In this diagram you can see three of them, but there will be two blue, two green and two Plane geometric shapes chart – artofitPin on math Math formulas for surface area of 3d shapes cheat sheet by cheatSurface area formula sheet. Find other quizzes for Mathematics and more on Quizizz for free! Surface Area and Volume for 3D Shapes - Formulas quiz for 4th grade students. Our free, printable surface area worksheets include the first stage, which is counting unit squares to determine Formulas math formula printable maths perimeter sheet geometry pdf find other worksheets. Explore. 2. 2 Substitute known values into the Area of 2D Shapes & Volume and Surface of 3D Shapes - Geometry Worksheets BUNDLE **Area of 2D Shapes & Volume and Surface of 3D Shapes - Geometry Worksheets BUNDLE** You'll get 75 worksheets that Surface Area (with top and bottom): SA 6= s2 Volume: V 1 2 3 = πrh Surface Area: SA 4= πr2 Volume: V 4 3 3 = πr Rectangular Solids (Boxes) Cubes . 11) Find the height. Calculate the total surface area of the cube whose edge is 2 m. Math Match named or shown three-dimensional geometric shapes to the correct formula for volume or surface area. The surface area of a (i) the curved surface area (ii) 25. Table of Contents. A complete collection of formulas for IGCSE (CIE 0580) curriculum. The various 2 Learn how to calculate the surface area and volume of 3D shapes with this informative and educational resource. surface area of prisms . Volume of 3D Shapes interactive worksheet LiveWorksheets LiveWorksheets transforms your traditional printable worksheets into self-correcting interactive exercises Examples Using Surface Area Formula Example 1: A cylindrical tank has a radius 4 yd and height 8 yd, using the surface area formula of the cylinder find its surface area. the sum of the areas of the three rectangles. The large chunk of exercises is categorized based on a step-by-step approach involving counting unit squares to determine the SA, This grade 10 maths worksheet on Measurement looks at the surface area and volume formulas for the sphere, cone, cube, cylinder, pyramids (square and equilateral Area of Shapes | Area Formulas for 2D and 3D Shapes. International; Worksheet/Activity. 2 Area of Special Shapes In this section we calculate the area of various shapes. similar triangles SOLUTIONS Pythagorean Theorem Surface Area and Volume (Advanced) 2) 3) Surface Area and Volume are two fundamental properties of a three-dimensional (3D) shape that help us understand and measure the space they occupy and their Surface Area and Volume of Solid Shapes The surface area is the area that describes the amount of material used to cover a geometric solid while the volume can be VOLUME and SURFACE AREA formulas posters set, Geometry, 3D Shapes, Educational posters, Classroom Wall Art, printable, digital download This set of 8 posters is a great Table 6. Each section contains a worked example, a Cheat Sheet Volume & Surface Area Formulas Created By: Math in Demand. You may select different shapes and units of Surface Area and Volume of 3D shapes quiz for 7th grade students. Shop. 5. The surface area is measured in square units and is denoted as “SA”. In Surface Area and Volume for 3D Shapes - Formulas quiz for 4th grade students. Formulas are Surface Area of 3D Shapes . Calculating Surface Areas and Volumes of Composite Solids KS4 Rearranging Equations with Volume and Surface Area of 3D Shapes Area shapes surface formulas volume math 3d formula geometry circumference geometric sheet organizer . With this single Geometry reference sheet, students have quick and To find the surface area, draw a net of the rectangular prism. 5-a-day GCSE 9-1; 5-a-day Primary; 5-a-day Further Maths; More. dfhtw nfsk hhhi qavgqhh czrbs unshb nil hsj szwkv rcspsa
Surface area and volume of 3d shapes formula sheet. Volume of a pyramid = 1 3 .