Question

A container in form of a frustum of a cone is 16 cm in diameter at the open end and 24 cm diameter at the bottom. If the vertical depth of the container is 8 cm calculate the capacity of the container.

Answer 1

The capacity of the container is 2546.78 cm³.

Explanation:

The volume of the frustum of a cone is:

`\text{Volume}=(\pi h)/(3)\cdot[R^(2)+Rr+r^(2)]`

The information provided is:

r = 16/2 = 8 cm

R = 24/2 = 12 cm

h = 8 cm

Compute the capacity of the container as follows:

`\text{Volume}=(\pi h)/(3)\cdot[R^(2)+Rr+r^(2)]`

`=(\pi\cdot8)/(3)\cdot[(12)^(2)+(12\cdot 8)+(8)^(2)]\\\\=(8\pi)/(3)* [144+96+64]\\\\=(8\pi)/(3)*304\\\\=2546.784445\\\\\approx 2546.78`

Thus, the capacity of the container is 2546.78 cm³.