1 CONFIDENTIAL 1 Grade 8 Volume 1

2 Solid Geometry Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes are cubes, rectangular solids, prisms, cylinders, spheres, cones and pyramids. The three flat shapes of the triangle, rectangle, and circle may become solids by adding the third dimension of depth. The triangle becomes a cone; the rectangle, a rectangular solid; and the circle, a cylinder.

3 Cubes A cube is a three-dimensional figure with all edges of the same length. s s s If s is the length of sides of the cube, Volume of the cube = s 3 Cuboids l w h If l is the length, w is the width and h is the height of the cuboids, Volume of the cuboids = lbh

4 Cylinders A cylinder is a solid with two congruent circles joined by a curved surface. In the given figure, the radius of the circular base is r and the height is h. The volume of the cylinder is the area of the base × height. The volume of the cylinder =Πr 2 h. r h Spheres A sphere is a solid with all its points the same distance from the center. r If r is the length of radius of the sphere, Volume of the sphere = 4Πr 3 3

5 A circular cone has a circular base, which is connected by a curved surface to its vertex. A cone is called a right circular cone, if the line from the vertex of the cone to the center of its base is perpendicular to the base.. Cones If r is the radius and h is the height, Volume of the cone = 1Πr 2 h 3 r h

6 b b hs Regular square pyramid Volume of the Regular square pyramid = 1b 2 h 3

7 Let us do some practice problems!

8 CONFIDENTIAL 8 1) What is volume of the cube with length of sides = 7 cm? a)343 cm 3 b)345 cm 3 c)347 cm 3 d)349 cm 3 a) 343 cm 3

9 CONFIDENTIAL 9 2) What is the volume of the cuboid with length 7 cm, width 4 cm and height 6 cm. a)162 cm 3 b)164 cm 3 c)166 cm 3 d)168 cm 3

10 CONFIDENTIAL 10 3) What is the volume of the cylinder with radius of the base is 8 cm and the height is 10 cm? a) cm 3 b) cm 3 c) cm 3 d) cm 3 c) cm 3 8cm 10 cm

11 CONFIDENTIAL 11 4) Which of the given boxes has the greatest volume? a)Box A b)Box B c)Box C d)All have equal volume A B C 1ft 4ft 2ft 3ft 6ft 2ft b) Box B

12 CONFIDENTIAL 12 5) This net can be folded on the dashed lines to make a box. What is the volume of the box? a)370 in 3. b)270 in 3. c)360 in 3. d)250 in 3. b) 270 in 3

13 CONFIDENTIAL 6) What is the volume of the sphere with radius = 6 cm? a) cm 3 b) cm 3 c) cm 3 d) cm 3 a) cm 3 6cm

14 CONFIDENTIAL 14 7) What is the volume of the cone with radius 6 cm and the height is = 12 cm? (Use Π = 3.14) a) cm 3 b) cm 3 c) cm 3 d) cm 3 6cm 12

15 CONFIDENTIAL 15 8) The rectangular prism at the right is made from centimeter cubes. What is the volume of the prism? a)88 cm 3 b)64 cm 3 c)48 cm 3 d)76 cm 3 c) 48 cm 3

16 CONFIDENTIAL 16 9) What is the volume of the regular square pyramid with base 11 cm and the height 12 cm? a)481 cm 3 b)483 cm 3 c)482 cm 3 d)484 cm 3 11cm 12cm

17 CONFIDENTIAL 17 10) What is the volume of a cone, if the diameter of the cone is 12.4 cm. and the height of the cone is 30 cm ? (Use Π = 3.14) a)1205 cm 3 b)1206 cm 3 c)1207 cm 3 d)1208 cm cm 30 c) 1207 cm 3

18 Assessment

19 CONFIDENTIAL 19 1) A metal cube of edge 9 cm is melted and formed into 2 smaller cubes. If the edge of one smaller cube is 6 cm, what the side of the second smaller cube? a)6 cm b)4 cm c)7 cm d)8 cm

20 CONFIDENTIAL 20 2) Three cuboids of dimensions 2cm x 5cm x 7cm, 4cm x 4cm x 5cm and 2cm x 3cm x 11cm are melted and a cube is formed. What is the side of the cube? a)8 cm b)6 cm c)7 cm d)9 cm b) 6 cm

21 CONFIDENTIAL 21 3) What is the volume of the cylinder with radius of the base is 10 cm and the height is 13 cm? a)4082 cm 3 b)4084 cm 3 c)4086 cm 3 d)4088 cm 3 10cm 13 cm a) 4082 cm 3

22 CONFIDENTIAL 22 4) What is the length of each edge of the box that is a perfect cube with volume 512 units 3 ? a)6 units b)5 units c)8 units d)7 units c) 8 units

23 CONFIDENTIAL 23 5) What is the volume of the given rectangular pyramid? a)892 cm 3 b)972 cm 3 c)794 cm 3 d)772 cm 3 b) 972 cm 3

24 CONFIDENTIAL 24 6) What is the volume of the sphere with radius = 13 cm? a) cm 3 b) cm 3 c) cm 3 d) cm 3 13cm d) cm 3

25 CONFIDENTIAL 25 7) Which of the given boxes has the least volume? a)Box A b)Box B c)Box C d)All have equal volume A B C 3ft 5ft 4ft 5ft 3ft a) Box A

26 CONFIDENTIAL 26 8) What is the volume of the cone with radius 5 cm and the height is = 9 cm? a)235.5 cm 3 b)232.5 cm 3 c)237.5 cm 3 d)231.5 cm 3 5 cm 9 a) cm 3

27 CONFIDENTIAL 27 9) What is the volume of the regular square pyramid with base 7 cm and the height 9 cm? a)143 cm 3 b)145 cm 3 c)147 cm 3 d)149 cm 3 7cm 9 cm c) 147 cm 3

28 CONFIDENTIAL 28 10) What is the volume of the given box? a)42 cm 3 b)52 cm 3 c)92 cm 3 d)102 cm 3 a) 42 cm 3

29 You did a great job today!