A frustum of a right circular cone has a height of $10 \mathrm {~m}$, a base of radius $2 \mathrm {~m}$, and a top of radius $1 \mathrm {~m}$. Find its volume.
A) $\frac { 7 } { 3 } \pi$
B) $\frac { 70 } { 3 } \pi$
C) $70 \pi$
D) $7 \pi$

Question

Quizplus · Accepted Answer

The formula for the volume of the frustum of a cone is:
$$V = \frac{1}{3}\pi h (R^2 + r^2 + Rr)$$
where
$h$ = height of frustum
$R$ = radius of base of frustum
$r$ = radius of top of frustum

Substitute the given values into the formula and simplify:
$$V = \frac{1}{3}\pi (10)(2^2 + 1^2 + (2)(1)) = \frac{70}{3}\pi$$

Therefore, the answer is B.

A Frustum of a Right Circular Cone Has a Height 10 m10 \mathrm {~m}10 m

A Frustum of a Right Circular Cone Has a Height $10 \mathrm {~m}$