Question

A large cone is cut into two parts, a smaller cone and a frustum of a cone.

The height of the large cone is 20 cm.
The height of the smaller cone is 4 cm.
The radius of the base of the large cone is 6 cm.
The radius of the base of the smaller cone is 4 cm.
Workout the volume of the frustum.​

Answer 1

volume of smaller cone:

`= 67.02 {cm}^(3)`

volume of larger cone:

`= 753.98 {cm}^(3)`

frustum:

`= 686.96 {cm}^(3)`

Answer 2

given:

radius of small cone= 4 cm

radius of large cone= 6 cm

height of small cone= 4 cm

height of large cone= 20 cm

solution:

big:

`v = (1)/(3) \pi {r}^(2) h`

`v = (1)/( 3) * \pi * {6}^(2) * 20`

`v = 753.98 \: {cm}^(3)`

small:

`v = (1)/( 3 ) \pi {r}^(2) h`

`v = (1)/(3) * \pi * {4}^(2) * 4`

`v = 67.02 \: {cm}^(3)`

frustum:

`v = 753.98 - 67.02`

`v = 686.96 \: {cm}^(3)`