Question

From a right circular cone of height 5 cm, a frustum with a base of radii 2 cm and 6 cm is obtained. What is the volume of the frustum?

a) 8/3π cm³
b) 32/3 π cm³
c) 64/3π cm³
d) 128/3π cm³

Answer 1

To find the volume of the frustum, calculate the volumes of the larger and smaller cones, then subtract the smaller cone's volume from the larger cone's volume using the formula for the volume of a cone (V = πr²h/3).

Step-by-step explanation:

To find the volume of the frustum, we need to calculate the volume of the larger cone and the smaller cone, and then subtract the smaller cone's volume from the larger cone's volume.

The volume of a cone can be found using the formula V = πr²h/3, where r is the radius and h is the height.

First, we calculate the volume of the larger cone with radius 6 cm: V1 = π(6 cm)²(5 cm)/3 = 60π cm³.

Next, we calculate the volume of the smaller cone with radius 2 cm: V2 = π(2 cm)²(5 cm)/3 = 20π cm³.

Finally, we subtract the volume of the smaller cone from the larger cone: Volume of frustum = V1 - V2 = 60π cm³ - 20π cm³ = 40π cm³.