Question

The radii of two circular ends of a frustum of a cone shaped dustbin are 15cm and 8cm. If its depth is 63cm, find the volume of the dustbin.

Answer 1

Hint: We are given the radius and height of the bucket. We will substitute the values in the formula of the frustum, which is $V=\dfrac{\pi }{3}h\left( {{R}^{2}}+Rr+{{r}^{2}} \right)$ , where $r$ and $R$ are the radii of the frustum and $h$ is the height of the frustum.

Complete step-by-step solution:
We are given the radii of two ends of the dustbin in the shape of a frustum. We have to find the volume of this dustbin. As we know that the volume of frustum is given as: $V=\dfrac{\pi }{3}h\left( {{R}^{2}}+Rr+{{r}^{2}} \right)$.

Substitute 15 for $R$, 8 for $r$ and 63 for $h$ in the above equation. So, we will get,
$\begin{align}
  & V=\dfrac{\pi \left( 63 \right)}{3}\left( {{\left( 15 \right)}^{2}}+\left( 15 \right)\left( 8 \right)+{{\left( 8 \right)}^{2}} \right) \\
 & =21\left( 225+120+64 \right).\pi \\
 & =21\left( 409 \right)\pi \\
 & =8589\pi \\
\end{align}$
Now substituting the value of $\pi =\dfrac{22}{7}$ , we will get,
$V=8589\times \dfrac{22}{7}=26,969.46c{{m}^{3}}$.
Hence the volume of the frustum is $26,969.46c{{m}^{3}}$.

Note:Volume of an object gives the amount of space enclosed by that object. Volume is always measured in cubic units. Students must know the formula of the volume of the frustum and substitute the values correctly in order to get the correct answer.