1. 1 CONFIDENTIAL 1 Grade 8 Volume 2

2. 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. 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 = lwh

4. 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. 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. 6 b b hs Regular square pyramid Volume of the Regular square pyramid = 1b 2 h 3

7. 7 Let us do some practice problems!

8. 8 CONFIDENTIAL 8 1) The perimeter of one face of a cube is 36 cm. What is its volume? a)725 cm 3 b)729 cm 3 c)766 cm 3 d)788 cm 3

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

10. 10 CONFIDENTIAL 10 3) What is the volume of the given cylinder? a)749.7 cm 3 b)422.7 cm 3 c)522.42 cm 3 d)649.7 cm 3

11. 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 4ft 9ft 7ft 9ft 5ft

12. 12 CONFIDENTIAL 5) Which of the following statement about the boxes is true? a)Volume A = Volume of B b)Volume of A > Volume of B c)Volume of A = Volume of C d)Volume of C > Volume of B A B C 4 4 4 2 6 5 5 1 7

13. 13 CONFIDENTIAL 6) What is the volume of the given sphere? a)5572.45 cm 3 b)5906.5 cm 3 c)5508.5 cm 3 d)5510.5 cm 3

14. 14 CONFIDENTIAL 14 7) What is the volume of the cone with radius 9 in and the height is = 15 in? a)4271.7 in 3 b)3271.7 in 3 c)2271.7 in 3 d)1271.7 in 3

15. 15 CONFIDENTIAL 15 8) Each small cube in the rectangular prism below has edges of length 2 centimeters. What is the volume of the prism in cubic centimeters? a)388 cm 3 b)292 cm 3 c)192 cm 3 d)576 cm 3

16. 16 CONFIDENTIAL 16 9) What is the volume of the given regular square pyramid ? a)30.3 m 3 b)31.3 m 3 c)32.3 m 3 d)33.3 m 3

17. 17 CONFIDENTIAL 17 10) What is the volume of a given cone if radius is 4 mm and height is 8 mm? a)134 mm 3 b)136 mm 3 c)138 mm 3 d)140 mm 3

18. 18 Assessment

19. 19 CONFIDENTIAL 19 1) What is the volume of the given box? a)40 in 3 b)80 in 3 c)70 in 3 d)60 in 3

20. 20 CONFIDENTIAL 20 2) If the length of each side of the cube is doubled, how does it affect the volume? a)The volume is increased by 6 times. b)The volume is increased by 9 times. c)The volume is increased by 8 times. d)The volume is increased by 4 times. 1ft

21. 21 CONFIDENTIAL 3) What is the volume of the cylinder with radius of the base is 10 cm and the height is 13 cm? a)308.2 cm 3 b)206.4 cm 3 c)128.6 cm 3 d)125.6 cm 3

22. 22 CONFIDENTIAL 22 4) What is the length of each edge of the box that is a perfect cube with volume 4096 units 3 ? a)15 units b)16 units c)18 units d)17 units

23. 23 CONFIDENTIAL 23 5) Which of the following statement about the boxes is false? A B C 5 5 5 3 7 6 5 2 12 a)Volume of A > Volume of B b)Volume of B > Volume of C c)Volume of A > Volume of C d)Volume of A < Volume of B

24. 24 CONFIDENTIAL 24 6) What is the volume of the sphere with radius = 5.5 cm? a)691.67 cm 3 b)693.67 cm 3 c)696.56 cm 3 d)699.67 cm 3 5.5cm

25. 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 6ft 4ft 5ft 8ft 4ft

26. 26 CONFIDENTIAL 26 8) What is the volume of the cone with radius 28 cm and the height is = 60 cm? a)49235.2 cm 3 b)49245.2 cm 3 c)49255.2 cm 3 d)49265.2 cm 3

27. 27 CONFIDENTIAL 27 9) What is the volume of the regular square pyramid with base 8 cm and the height 10 cm? a)243.2 cm 3 b)145.3 cm 3 c)213.3 cm 3 d)149.3 cm 3 8cm 10 cm

28. 28 CONFIDENTIAL 28 10) What is the volume of the given box? a)96 cm 3 b)92 cm 3 c)94 cm 3 d)102 cm 3

29. 29 You did a great job today!