Grade 8 Volume 1 CONFIDENTIAL 1

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.

Cubes A cube is a three-dimensional figure with all edges of the same length. s If s is the length of sides of the cube , Volume of the cube = s3 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

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 =Πr2h. 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 = 4Πr3 3

If r is the radius and h is the height, Cones 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. . r h If r is the radius and h is the height, Volume of the cone = 1Πr2h 3

Regular square pyramid b h s Volume of the Regular square pyramid = 1b2h 3

Let us do some practice problems!

1) What is volume of the cube with length of sides = 7 cm? CONFIDENTIAL 8

2) What is the volume of the cuboid with length 7 cm, width 4 cm and height 6 cm. 9 CONFIDENTIAL

3) What is the volume of the cylinder with radius of the base is 8 cm and the height is 10 cm? (Use Π = 3.14) 2008.6 cm3 2019.6 cm3 2009.6 cm3 2109.6 cm3 8cm 10cm CONFIDENTIAL 10

4) Which of the given boxes has the greatest volume? Box A Box B Box C All have equal volume CONFIDENTIAL 11

5) This net can be folded on the dashed lines to make a box 5) This net can be folded on the dashed lines to make a box. What is the volume of the box? 370 in3. 270 in3. 360 in3. 250 in3. CONFIDENTIAL 12

6) What is the volume of the sphere with radius = 6 cm? (Use Π = 3.14) CONFIDENTIAL

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

8) The rectangular prism at the right is made from centimeter cubes 8) The rectangular prism at the right is made from centimeter cubes. What is the volume of the prism? 88 cm3 64 cm3 48 cm3 76 cm3 CONFIDENTIAL 15

9) What is the volume of the regular square pyramid with base 11 cm and the height 12 cm? CONFIDENTIAL 16

10) What is the volume of a cone, if the diameter of the cone is 12 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) 12.4cm 30 1205 cm3 1206 cm3 1207 cm3 1208 cm3 CONFIDENTIAL 17

Assessment

1) A metal cube of edge 9 cm is melted and formed into 2 smaller cubes 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? 6 cm 4 cm 7 cm 8 cm CONFIDENTIAL 19

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? 8 cm 6 cm 7 cm 9 cm CONFIDENTIAL 20

3) What is the volume of the cylinder with radius of the base is 10 cm and the height is 13 cm? CONFIDENTIAL 21

4) What is the length of each edge of the box that is a perfect cube with volume 512 units3? CONFIDENTIAL 22

5) What is the volume of the given rectangular pyramid? 892 cm3 972 cm3 794 cm3 772 cm3 CONFIDENTIAL 23

6) What is the volume of the sphere with radius = 13 cm? CONFIDENTIAL 24

7) Which of the given boxes has the least volume? Box A Box B Box C All have equal volume CONFIDENTIAL 25

8) What is the volume of the cone with radius 5 cm and the height is = 9 cm? CONFIDENTIAL 26

9) What is the volume of the regular square pyramid with base 7 cm and the height 9 cm? CONFIDENTIAL 27

10) What is the volume of the given box? 42 cm3 52 cm3 92 cm3 102 cm3 CONFIDENTIAL 28

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