Solid Geometry IIBy V. Murali

Volume of cone

Volume of cone = r2h

Example 1Calculate the volume of a cone with 16 cm base radius and 24 cm height. ( = 3.142).

Solution

Volume of cone = r2h

= x 3.142 x (16 cm)2 x 24 cm

= 6434.82 cm3

Example 2The volume a cone is 425 cm3. If the base radius is 8 cm, calculate the height of the cone. ( = 3.142)

Solution

Radius ( r )

Height ( h )

16 cm

24 cm

8 cm

? cm

Volume of cone,V = r2h

h =

=

= 6.34 cm

Example 2The volume a cone is 684 cm3. If the height of the cone is 9 cm, calculate its base radius. ( = 3.142)

Solution

Volume of cone,V = r2h

r =

=

= 8.52 cm

Volume of sphere and hemisphere

Volume of sphere = r3

Example 3

Calculate the volume of a sphere with 21 cm radius. ( = )

radius

? cm

9 cm

Solution

Volume of sphere = r3

= x x (21 cm)3

= 38 808 cm3

Example 4

Calculate the volume of a hemisphere with 14 cm radius. ( = )

Solution

Volume of hemisphere = x r3

= x x x (14 cm)3

= 5749.33 cm3

Example 5Volume of a sphere is 20 cm3. Calculate the radius of the sphere. ( = 3.142)

Solution

Volume of sphere,V = r3

r =

=

= 1.68 cm

21 cm

14 cm

Example 6Volume of a hemisphere is 32 cm3. Calculate the radius of the hemisphere. ( = 3.142)

Solution

Volume of hemisphere,V = r3

r =

=

= 2.17 cm

Volume of sphere and hemisphere

Volume of composite solids involved cuboids, cubes, prisms, cylinders, cones, sphere and hemisphere can be calculated by:

1. calculate each solid separately, then2. sum up the volume of the solids

Example 7Calculate the volume of the composite solid below, given the base radius of the cone and the height of the cone are 3 cm and 12 cm respectively. ( = 3.142)

Volume of hemisphere = r3

= x 3.142 x (10 cm)3

= 2094.67 cm3

Volume of cone = r2h

= x 3.142 x (3 cm)2 x 12 cm

= 113.11 cm3

So, the volume of the composite solid = 2094.67 cm3 + 113.11 cm3

= 2207.78 cm3

10 cm

Test yourself1. Calculate the volume of the cone below.

2. Volume of a cone is 3124 cm3. If its height is 15 cm, calculate the base radius of the cone. ( = 3.142)

3. Diameter of a sphere shaped ball is 12 cm. Calculate its volume. ( = 3.142)4. Calculate the volume of the composite solid below:

Answers1. 307.92 cm3

2. 14.14 cm3. 904.90 cm3

4. 6618.86 cm3

20 cm

9 cm

6 cm

14 cm