11. A polyhedron is said to be concave if at least one angle between any of its two edges is a reflex angle.
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1 BOOK 8 ( CBSE / Chap10 /Visualizing Solid Shapes Chapter Facts. 1. A plane figure has two dimensions (2 D and a solid figure has three dimensions ( 3 D. 2. Some solid shapes consist of one figure embedded in the other ( cylinder with a conical grove or combination of two figures ( cone mounted on a cylinder. Such solids are called nested solids. 3. 3D objects have different views (front-view, top view and side view from different positions. 4. A map is different from a picture. It depicts the location of a particular object/place in relation to other objects/places. Symbols are used to depict the different objects/places. 5. Maps involve a scale which is fixed for a particular map. 6. Perspective is very important for drawing a picture but is not relevant for a map. 7. The corners of a solid shape are called its vertices; the line segments of its skeleton are its edges; and its flat surfaces are its faces. 8. A solid all whose faces are polygons is called a polyhedron. Cube, cuboid,, pyramid are examples of polyhedrons. 9. A solid having a surface which is not a polygon is not a polyhedron. Cone, sphere, cylinder are not polyhedrons. 10. A polyhedron is said to be convex if angle between any of its two edges is less than 180 o. 11. A polyhedron is said to be concave if at least one angle between any of its two edges is a reflex angle.
2 12. A polyhedron is said to be regular if its faces are made up of regular polygons and the same number of faces meet at each vertex. A cube is a regular polygon as all faces are identical. A cuboid is not regular because all faces are not identical. 13. A is a solid shape whose base and top are congruent polygons and lateral faces are parallelograms in shape. 14. A right is a solid with congruent polygons on top and bottom and rectangles on sides. Some s are. : Triangular Rectangular Square Pentagonal Hexagonal A cube can be called a square. A cuboid can be called a rectangular. 14. A pyramid is a solid shape whose base is a polygon and lateral faces are triangles with common vertex. Some pyramids are : Triangular pyramid Square pyramid Rectangular pyramid Pentagonal pyramid Base is a triangle Base is a square Base is a rectangle Base is a pentagon 15. For any polyhedron, F + V E = 2 where F stands for number of faces, V stands for number of vertices and E stands for number of edges. This relationship is called Euler s formula. A Multiple Choice Questions Formative Assessment Tick ( the correct answer for each of the following :
3 1. The other name of a triangular pyramid is (a tetrahedron (b octahedron (c cuboid (d cube 2. Four vertices are found in (a triangular (b square pyramid (c rectangular pyramid (d triangular pyramid 3. Number of edges in a rectangular pyramid is (a 7 (b 8 (c 9 (d The number of vertices in a triangular is (a 6 (b 8 (c 5 (d 7 5. How many faces are there in a pyramid whose base is a polygon of 6 sides? (a 6 (b 12 (c 8 (d How many vertices are there in a whose base is a polygon of 5 sides? (a 10 (b 12 (c 14 (d 15 B Fill in the blanks: 1. A tetrahedron has faces, edges and vertices. 2. The are used to depict the object/places in a map. 3. A cube can be called a. 4. Perspective is very important for drawing a but is not relevant for a. 5. A polyhedron is said to be if at least one angle between any of its two edges is a reflex angle. C True / False Say true or false for each of the following. 1. Maps involve a scale which is fixed for a particular map. T/F 2. 3D objects may have different views from different positions. T/F 3. A cuboid can be called a rectangular. T/F 4. The distances shown on a map are proportional to the actual distances on the ground. T/F D True / False with Justification : Say true or false for each of the following. Justify your answer?
4 1. A cuboid is not a regular polygon. T/F 2. A is a solid with congruent polygons on top and bottom and rectangles on sides. T/F E Matching Match the items in column I with items in column II. Column I Column II (i A Concave polyhedron (ii B Hexagonal pyramid (iii C Triangular bi pyramid (iv D Square (v E Pentagonal (vi F Pentagonal Pyramid. G Nested solid Summative Assessment A One mark questions 1. A polyhedron has 10 faces and 5 vertices. Find the number of edges it has. 2. A polyhedron has 12 faces and 18 edges. Find the number of vertices it has. 3. A polyhedron has 7 vertices and 14 edges. Find the number of faces it has. 4. Is it possible to have a polyhedron with 7 faces, 5 vertices and 9 edges?
5 5. Is it possible to have a polyhedron with 9 faces, 6 vertices and 13 edges? B Two mark questions 1. Draw side and top view for the following Side view Top view 2. Draw side and front view for the following Side view Front view 3. Draw top and front view for the following Top view Front view C Three mark questions Draw front, side and top view for each of the following Front view Side view Top view 1 2
6 Verify the Euler s formula for each of the following polyhedrons. 3 F =, V = E = 4 F =, V = E = 5 F =, V = E = 6 F =, V = E = 7 F =, V = E = D Four mark questions Draw the object whose front, side and top views are given. ( Front view Side view Top view Object 2 End
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