Question

The perimeter of the ends of a frustum of a cone are $44cm$ and $8.4\pi cm$. If the depth is $14cm$, then find its volume.

• A. $1408.6{cm}^3$
• B. $1486{cm}^3$
• C. $1406{cm}^3$
• D. None of these

Answer 1

The correct option is A $1408.6{cm}^3$

Let the bottom and top radius be $R$ and $r$ respectively

Perimeter of the ends of the frustum cone

$2\pi R=44cm\Rightarrow R=7cm$

$2\pi r=8.4\pi cm\Rightarrow r=4.2cm$

$depth\left(h\right)=14cm$

We know that the volume of the frustum cone

$=\frac{1}{3}\pi (R^2+r^2+Rr)h$

So,

$=\frac{1}{3}\times \frac{22}{7}(7^2+(4.2{)}^2+7\times 4.2)\times 14$

$=\frac{1}{3}\times 22\times (49+17.64+29.4)\times 2$

$=\frac{44}{3}\times \left(96.04\right)$

$=1408.6c{m}^3$