Solve the problem.
-A frustum of a right circular cone has a height of 10 m, a base of radius 5m, and a top of radius 4m. Find its volume.
A) $\frac { 61 } { 3 } \pi$
B) $61 \pi$
C) $610 \pi$
D) $\frac { 610 } { 3 } \pi$

Question

Solve the problem.
-A frustum of a right circular cone has a height of 10 m, a base of radius 5m, and a top of radius 4m. Find its volume. 
A) $\frac { 61 } { 3 } \pi$
B) $61 \pi$
C) $610 \pi$
D) $\frac { 610 } { 3 } \pi$

Quizplus · Accepted Answer

The volume of a frustum of a cone is given by 
$$\frac { 1 } { 3 } \pi h\left( r_{ 1 }^{ 2 }+r_{ 2 }^{ 2 }+r_{ 1 }r_{ 2 } \right)$$
where $h$ is the height of the frustum, $r_{1}$ and $r_{2}$ are the radii of the base and top of the frustum, respectively.

Substituting the given values, we have
$$\frac { 1 } { 3 } \pi \times 10 \times \left( 5^{ 2 }+4^{ 2 }+5\times 4 \right).$$
This simplifies to $\frac{610}{3}\pi$, which is option D.

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