Page 1 Points to Remember : 1. Solid. An object that has a fixed shape and size is caled a solid. A solid occupies a fixed amount of space. Solids occur in different shapes. These shapes are known as three- dimensional shapes. The various types of these shapes are shown below. 2. Cuboid. Solids such as a wooden box, a matchbox, a brick, a book, an almirah, etc., are all in the shape of a cuboid. Some of these shapes are given below. A cuboid has length, breadth and height. Various parts of a cuboid are given below : (i) Faces. A cuboid has six rectangular faces. The opposite faces of a cuboid are identical. (ii) Edges. Two adjacent faces of a cuboid meet in a line segment, called an edge of the cuboid. A cuboid has 12 edges. (iii) Vertices. Three edges of a cuboid meet at a point, called a vertex. A cuboid has 8 vertices. Thus, a cuboid has 6 rectangular faces, 12 edges and 8 vertices. 3. Cube. A cuboid whose length, breadth and height are equal is called a cube. Page 2 Points to Remember : 1. Solid. An object that has a fixed shape and size is caled a solid. A solid occupies a fixed amount of space. Solids occur in different shapes. These shapes are known as three- dimensional shapes. The various types of these shapes are shown below. 2. Cuboid. Solids such as a wooden box, a matchbox, a brick, a book, an almirah, etc., are all in the shape of a cuboid. Some of these shapes are given below. A cuboid has length, breadth and height. Various parts of a cuboid are given below : (i) Faces. A cuboid has six rectangular faces. The opposite faces of a cuboid are identical. (ii) Edges. Two adjacent faces of a cuboid meet in a line segment, called an edge of the cuboid. A cuboid has 12 edges. (iii) Vertices. Three edges of a cuboid meet at a point, called a vertex. A cuboid has 8 vertices. Thus, a cuboid has 6 rectangular faces, 12 edges and 8 vertices. 3. Cube. A cuboid whose length, breadth and height are equal is called a cube. Examples. Ice cubes, sugar cubes, dice, etc., are all examples of a cube. Clearly, a cube like cuboid has 6 square faces, 12 edges and 8 vertices. 4. Cylinder. Objects such as a circular pillar ; a circular pipe, a test tube, a circular storage tank, a measuring jar ; a gas cylinder, a circular powder tin, etc., are in the shape of a cylinder. Some of these shapes are shown below. A cylinder has a curved lateral surface and two circular faces at its ends. A cylinder has no corner or vertex. A cylinder has two plane faces, namely the top and the base, and one curved face. It has 2 circular edges. The distance between its ends faces is called its length. 5. Cone. Objects such as an ice-cream cone, a conical tent, a conical vessel, a clown’ s cap, etc., are in the shape of a cone. Some examples of cones are given below. A cone has a plane circular end as the base and a curved surface tapering into a point, called its vertex. Thus, a cone has one plane face (i.e. base) and one curved face. It has one circular edge and one vertex. 6. Sphere. An object which is in the shape of a ball is said to have the shape of a sphere. A sphere has a curved surface. A sphere has no vertex and no edge. Page 3 Points to Remember : 1. Solid. An object that has a fixed shape and size is caled a solid. A solid occupies a fixed amount of space. Solids occur in different shapes. These shapes are known as three- dimensional shapes. The various types of these shapes are shown below. 2. Cuboid. Solids such as a wooden box, a matchbox, a brick, a book, an almirah, etc., are all in the shape of a cuboid. Some of these shapes are given below. A cuboid has length, breadth and height. Various parts of a cuboid are given below : (i) Faces. A cuboid has six rectangular faces. The opposite faces of a cuboid are identical. (ii) Edges. Two adjacent faces of a cuboid meet in a line segment, called an edge of the cuboid. A cuboid has 12 edges. (iii) Vertices. Three edges of a cuboid meet at a point, called a vertex. A cuboid has 8 vertices. Thus, a cuboid has 6 rectangular faces, 12 edges and 8 vertices. 3. Cube. A cuboid whose length, breadth and height are equal is called a cube. Examples. Ice cubes, sugar cubes, dice, etc., are all examples of a cube. Clearly, a cube like cuboid has 6 square faces, 12 edges and 8 vertices. 4. Cylinder. Objects such as a circular pillar ; a circular pipe, a test tube, a circular storage tank, a measuring jar ; a gas cylinder, a circular powder tin, etc., are in the shape of a cylinder. Some of these shapes are shown below. A cylinder has a curved lateral surface and two circular faces at its ends. A cylinder has no corner or vertex. A cylinder has two plane faces, namely the top and the base, and one curved face. It has 2 circular edges. The distance between its ends faces is called its length. 5. Cone. Objects such as an ice-cream cone, a conical tent, a conical vessel, a clown’ s cap, etc., are in the shape of a cone. Some examples of cones are given below. A cone has a plane circular end as the base and a curved surface tapering into a point, called its vertex. Thus, a cone has one plane face (i.e. base) and one curved face. It has one circular edge and one vertex. 6. Sphere. An object which is in the shape of a ball is said to have the shape of a sphere. A sphere has a curved surface. A sphere has no vertex and no edge. 7. Triangular prism. A solid whose lateral faces are rectangular and the bases are congruent triangles, is called a triangular prism. The adjoining figure shows a triangular prism, denoted by (ABC, PQR). A triangular prism has 6 vertices, 3 rectangular lateral faces, 2 triangular bases and 9 edges. 8. Pyramid. A pyramid is a solid whose base is a plane rectilinear figure and whose side faces are triangles having a common vertex, called the vertex of the pyramid. The length of perpendicular drawn from the vertex of a pyramid to its base is called the height of the pyramid. The side faces of a pyramid are called its lateral faces. (i) Square pyramid. A solid whose base is a square and whose side faces are triangles having a common vertex is called a square pyramid. The adjacent figure shows a square pyramid OABCD with O as vertex, the square ABCD as its base and OP as its height. A square pyramid has 4 lateral triangular faces and 8 edges. (ii) Triangular pyramid. A solid whose base is a triangle and whose side faces are triangles having a common vertex is called a triangular pyramid. The adjacent figure shows a triangular pyramid OABC with O as vertex and ABC as its base. A triangular pyramid has 3 triangular lateral faces, one triangular base and 6 edges. A triangular pyramid is also called a tetrahedron. Tick ( ) the correct answer in each of Q. 1 to Q. 6. Q. 1. A cuboid has (a) length only (b) length and breadth only (c) length, breadth and height (d) thickness only Q. 2. A dice is an example of a (a) cuboid (b) cube (c) cone (d) cylinder Q. 3. A gas pipe is an example of a (a) cuboid (b) cube (c) cone (d) cylinder Q. 4. A football is an example of a (a) cylinder (b) cone (c) sphere (d) none of these Q. 5 A brick is an example of a (a) cube (b) cuboid (c) prism (d) cylinder Q. 6. An ice-cone is an example of a (a) cuboid (b) cube (c) pyramid (d) none of these Sol. 1. (c) . . . A cuboid has three dimensions, length, breadth and height or depth. 2. (b) . . . Its six faces arc of square. 3. (d) . . . Its shape is of a cylinder as it is round in shape on either sides/faces. Page 4 Points to Remember : 1. Solid. An object that has a fixed shape and size is caled a solid. A solid occupies a fixed amount of space. Solids occur in different shapes. These shapes are known as three- dimensional shapes. The various types of these shapes are shown below. 2. Cuboid. Solids such as a wooden box, a matchbox, a brick, a book, an almirah, etc., are all in the shape of a cuboid. Some of these shapes are given below. A cuboid has length, breadth and height. Various parts of a cuboid are given below : (i) Faces. A cuboid has six rectangular faces. The opposite faces of a cuboid are identical. (ii) Edges. Two adjacent faces of a cuboid meet in a line segment, called an edge of the cuboid. A cuboid has 12 edges. (iii) Vertices. Three edges of a cuboid meet at a point, called a vertex. A cuboid has 8 vertices. Thus, a cuboid has 6 rectangular faces, 12 edges and 8 vertices. 3. Cube. A cuboid whose length, breadth and height are equal is called a cube. Examples. Ice cubes, sugar cubes, dice, etc., are all examples of a cube. Clearly, a cube like cuboid has 6 square faces, 12 edges and 8 vertices. 4. Cylinder. Objects such as a circular pillar ; a circular pipe, a test tube, a circular storage tank, a measuring jar ; a gas cylinder, a circular powder tin, etc., are in the shape of a cylinder. Some of these shapes are shown below. A cylinder has a curved lateral surface and two circular faces at its ends. A cylinder has no corner or vertex. A cylinder has two plane faces, namely the top and the base, and one curved face. It has 2 circular edges. The distance between its ends faces is called its length. 5. Cone. Objects such as an ice-cream cone, a conical tent, a conical vessel, a clown’ s cap, etc., are in the shape of a cone. Some examples of cones are given below. A cone has a plane circular end as the base and a curved surface tapering into a point, called its vertex. Thus, a cone has one plane face (i.e. base) and one curved face. It has one circular edge and one vertex. 6. Sphere. An object which is in the shape of a ball is said to have the shape of a sphere. A sphere has a curved surface. A sphere has no vertex and no edge. 7. Triangular prism. A solid whose lateral faces are rectangular and the bases are congruent triangles, is called a triangular prism. The adjoining figure shows a triangular prism, denoted by (ABC, PQR). A triangular prism has 6 vertices, 3 rectangular lateral faces, 2 triangular bases and 9 edges. 8. Pyramid. A pyramid is a solid whose base is a plane rectilinear figure and whose side faces are triangles having a common vertex, called the vertex of the pyramid. The length of perpendicular drawn from the vertex of a pyramid to its base is called the height of the pyramid. The side faces of a pyramid are called its lateral faces. (i) Square pyramid. A solid whose base is a square and whose side faces are triangles having a common vertex is called a square pyramid. The adjacent figure shows a square pyramid OABCD with O as vertex, the square ABCD as its base and OP as its height. A square pyramid has 4 lateral triangular faces and 8 edges. (ii) Triangular pyramid. A solid whose base is a triangle and whose side faces are triangles having a common vertex is called a triangular pyramid. The adjacent figure shows a triangular pyramid OABC with O as vertex and ABC as its base. A triangular pyramid has 3 triangular lateral faces, one triangular base and 6 edges. A triangular pyramid is also called a tetrahedron. Tick ( ) the correct answer in each of Q. 1 to Q. 6. Q. 1. A cuboid has (a) length only (b) length and breadth only (c) length, breadth and height (d) thickness only Q. 2. A dice is an example of a (a) cuboid (b) cube (c) cone (d) cylinder Q. 3. A gas pipe is an example of a (a) cuboid (b) cube (c) cone (d) cylinder Q. 4. A football is an example of a (a) cylinder (b) cone (c) sphere (d) none of these Q. 5 A brick is an example of a (a) cube (b) cuboid (c) prism (d) cylinder Q. 6. An ice-cone is an example of a (a) cuboid (b) cube (c) pyramid (d) none of these Sol. 1. (c) . . . A cuboid has three dimensions, length, breadth and height or depth. 2. (b) . . . Its six faces arc of square. 3. (d) . . . Its shape is of a cylinder as it is round in shape on either sides/faces. 4. (c) . . . Football is round as sphere. 5. (b) . . . A brick has length, breadth and height. 6. (d) . . . Its shape is like a cone. Ans. Q. 7. Fill in the blanks : (i) An object that occupies space is called a..... . (ii) A cuboid has........faces, .........edges and.........vertices. (iii) The.........faces of a cuboid are identical. (iv) A............has no vertex and no edge. (v) All the faces of a............are identical. (vi) A square pyramid has............lateral triangular faces and............edges. (vii) A triangular pyramid has........triangular lateral faces and............edges. (viii) A triangular prism has..........vertices, ..........rectangular lateral faces, ..........triangular bases and.........edges. Sol. (i) solid (ii) 6, 12 and 18 (iii) opposite (iv) sphere (v) cube (vi) 4, 8 (vii) 3, 6 (viii) 6, 3, 2, 9 Ans. Q. 8. Give examples of four objects which are in the shape of : (a) a cone (b) a cuboid (c) a cylinder. Sol. (a) A cone: (i) Conical cup (ii) An ice cream cup (iii) Conical tent house (iv) Conical vessel. (b) A cuboid : (i) A book, (ii) A brick, (iii) a box, (iv) a brief case. (c) A cylinder : (i) Circular pipe (ii) A jar or tumbler (iii) A round powder tin (iv) Circular piller.Read More

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