- \n
- Volume and Surface Area of Cuboid<\/li>\n
- Volume and Surface Area of Cube<\/a><\/li>\n
- Volume and Surface Area of Cube and Cuboid<\/li>\n
- Volume of Cuboid<\/a><\/li>\n
- Volume of Cube<\/a><\/li>\n
- Lateral Surface Area of a Cuboid<\/a><\/li>\n
- Cross Section<\/li>\n
- Cylinder<\/li>\n
- Right Circular Cylinder<\/li>\n
- Hollow Cylinder<\/li>\n
- Problems on Right Circular Cylinder<\/li>\n<\/ul>\n
What are Solid Figures?<\/h3>\n
Solid figures are nothing but three-dimensional geometric shapes such as cuboids, cubes, prisms, pyramids, spheres, etc. The 3D figures consist of faces, edges, and vertices. The flat part of a solid shape is known as the face. Each corner of the face is known as a vertex. The point where two faces meet is known as the edges. The solid figures contain three dimensions length, width, and height. Examples of solids figures are computers, dice, container, and so on.<\/p>\n
Types of Solid Figures<\/h3>\n
Cuboid:<\/strong> In geometry, a cuboid is a three-dimensional figure with six faces, 12 edges, and 8 vertices. A cuboid is a rectangular 3D box. The three dimensions of a cuboid are length, breadth, and height.
\n![\"cuboid\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/cuboid.png\")
<\/p>\nCube:<\/strong> Cube is a type of solid figure which is bounded by six faces, 8 vertices, and 12 edges. It consists of three dimensions length, width, and height. And the difference between the cube and cuboid is that all the sides of the cube are equal.
\n![\"cube\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/cube-1.png\")
<\/p>\nSphere:<\/strong> A sphere is a solid figure with no faces, no edges, and no vertices. It is a 3D figure. A sphere has one surface that is equidistant from the origin. An example of a sphere is the ball.
\n![\"sphere\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/sphere.png\")
<\/p>\nPrism:<\/strong> Prism is a 3D solid figure that consists of two equal ends, flat surfaces, and has an identical cross-section across its length. A prism has six vertices, 9 edges, and 5 faces.
\n![\"prism\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/prism.png\")
<\/p>\nPyramid:<\/strong> A pyramid is a solid figure with a flat base and all lateral faces as triangles. Types of pyramid are square pyramid, triangular pyramid, hexagonal pyramid, and pentagonal pyramid.
\n![\"pyramid\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/pyramid.png\")
<\/p>\nCylinder:<\/strong> A cylinder is a solid three-dimensional figure with two parallel circular bases that are joined by the curved surface. The shape of a cylinder has no vertices, two edges, 2 flat faces, and one curved face. We can measure the cylinder using the total surface area, curved surface area, and volume of the cylinder.
\n![\"cylinder\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/cylinder.png\")
<\/p>\nCone:<\/strong> A cone is a three-dimensional geometric shape that narrows from the flat base to the point. The base of a cone is a circle. It has one face. An example of the cone is ice cream, funnel, party hat.
\n![\"Cone\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/Cone.png\")
<\/p>\nAlso, Check:<\/p>\n
- \n
- Plane Figures<\/a><\/li>\n
- Rectilinear Figures<\/a><\/li>\n<\/ul>\n
Properties of Solid Shapes<\/h3>\n
1. Solid shapes or solid figures are three-dimensional geometric figures that means they have length, breadth, and height.
\n2. Solid figures have three dimensions.
\n3. They have the number of faces, edges, and vertices based on the figure.<\/p>\nSolid Figures Examples<\/h3>\n
Example 1.<\/strong>
\nFind the volume and surface area of a cuboid of length 5 cm, breadth 6 cm, and height 7 cm.
\nSolution:<\/strong>
\n![\"cuboid_1\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/cuboid_1.png\")
\nGiven that
\nlength= 5 cm
\nbreadth = 6 cm
\nheight = 7 cm
\nVolume of cuboid = V = l x b x h
\n= 5 x 6 x 7
\n= 210 cm\u00b3
\nSurface area of a cuboid = 2 ( lb + lh + bh)
\n= 2( 5×6 + 6×7 + 5×7)
\n=2(30 + 42 + 35)
\n=2(107)
\n= 142cm\u00b2
\nThus the surface area of a cuboid is 142cm\u00b2<\/p>\nExample 2.<\/strong>
\nFind the volume of the sphere of radius 28 cm.
\nSolution:<\/strong>
\nGiven that
\n![\"sphere_1\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/sphere_1.png\")
\nradius of the sphere = r = 28 cm
\nVolume of sphere = 4\/3 \u03c0r\u00b3
\n= (4\/3) \u00d7 (22\/7) \u00d7 28 \u00d7 28 \u00d7 28
\n= 4 \u00d7 22 \u00d7 28 \u00d7 28 x 4
\n= 275,968cm\u00b3
\nThus the volume of the sphere is 275,968cm\u00b3<\/p>\nExample 3.<\/strong>
\nThe base radius and height of a right circular cone is 7 cm and 24 cm. Find its curved surface area and volume
\nSolution:<\/strong>
\nGiven that
\n![\"Cone_1\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/Cone_1.png\")
\nRadius = r = 7 cm
\nHeight = h = 24 cm
\nSlant height = l = \u221a r\u00b2 + h\u00b2
\nl = \u221a7 \u00d7 7 + 24 \u00d7 24 cm
\n25 cm
\nCurved surface area = \u03c0rl
\n22\/7 \u00d7 7 \u00d7 25 cm\u00b2
\n550 cm\u00b2
\nTotal surface area = \u03c0rl + \u03c0r\u00b2
\n= (550 + 22\/7 + 49) cm\u00b2
\n= (550 + 154) cm\u00b2
\n= 704 cm\u00b2
\nVolume = \u2153\u03c0r\u00b2h
\n= \u2153 \u00d7 22\/7 \u00d7 49 \u00d7 24 cm\u00b3
\n= 1232 cm\u00b3
\nThus the volume of a cone is 1232 cm\u00b3<\/p>\nExample 4.<\/strong>
\nA conical tent is 3 high and its base radius is 4 cm. Find the cost of the canvas required to make the tent at the rate of Rs 60 per unit.
\nSolution:<\/strong>
\nGiven that
\n![\"Cone_2\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/Cone_2.png\")
\nRadius = r = 3
\nHeight = h = 4
\nSlant height = l = \u221ar\u00b2 + h\u00b2
\n= \u221a 9 + 16
\n= \u221a25
\n= 5
\nSlant height of the tent is 5
\nCurved surface area = \u03c0rl
\nWe know that \u03c0 = 3.14
\n= 3.14 \u00d7 4 \u00d7 5
\n= 62.8
\nTherefore canvas required for making the tent = 62.8
\nTherefore cost of the canvas at 65 per m\u00b2
\n= 65 \u00d7 62.8
\n= 4082<\/p>\nExample 5.<\/strong>
\nThe radius and height of the right circular cylinder are 7 cm and 10 cm. Find curved surface area, total surface area, and volume
\nSolution:<\/strong>
\nGiven that
\n![\"cylinder_1\"](\"https:\/\/eurekamathanswerkeys.com\/wp-content\/uploads\/2021\/11\/cylinder_1.png\")
\nRadius = r = 7 cm
\nHeight = h = 10 cm
\nThe curved surface area of a circular cylinder = 2\u03c0rh
\n= 2 \u00d7 22\/7 \u00d7 7 \u00d7 10 cm\u00b2
\n= 440 cm\u00b2
\nTotal surface area of a circular cylinder = 2\u03c0rh + 2 \u03c0r\u00b2
\n= 2 \u00d7 22\/7 \u00d7 7 \u00d7 10 + 2 \u00d7 22\/7 \u00d7 7 \u00d7 7 cm\u00b2
\n= 440 cm\u00b2 + 308 cm\u00b2 = 748 cm\u00b2
\nVolume of a circular cylinder = \u03c0rh
\n= 22\/7 \u00d7 7 \u00d7 10 cm\u00b2
\n= 1540 cm\u00b3
\nThus the volume of the cylinder is 1540 cm\u00b3<\/p>\nFrequently Asked Questions on Solid Figures<\/h3>\n
1. What is meant by solid figures?<\/strong><\/p>\n
In geometry, the solid shapes are the objects that occupy space. Examples of solid shapes are cube, cone, cuboid, sphere, cylinder.<\/p>\n
2. What is the measurement of a solid figure?<\/strong><\/p>\n
A solid figure has three dimensions while a plane figure has only two dimensions. The space enclosed by a solid figure is called its volume.<\/p>\n
3. How do you represent solid figures?<\/strong><\/p>\n
Three-dimensional solid figures can be represented by the two-dimensional pattern of polygons that create them.<\/p>\n","protected":false},"excerpt":{"rendered":"
Hello students!!! Would you like to know what is meant by solid figures? If yes, then what are you waiting for you are on the right page. Start your preparation by using this page. In this article, the students of 9th grade can find the topics related to solid figures and their measurements. Usually, we … Read more<\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143784"}],"collection":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/comments?post=143784"}],"version-history":[{"count":2,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143784\/revisions"}],"predecessor-version":[{"id":143787,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/posts\/143784\/revisions\/143787"}],"wp:attachment":[{"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/media?parent=143784"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/categories?post=143784"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ccssanswers.com\/wp-json\/wp\/v2\/tags?post=143784"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- Rectilinear Figures<\/a><\/li>\n<\/ul>\n