Question

If the radii of the circular ends of a conical bucket $45\mathrm{cm}$ high are $28\mathrm{cm}$ and $7\mathrm{cm}$, find the capacity of the bucket.

Answer 1

Determine the volume of the conical bucket:

The volume $\left(V\right)$ of the conical bucket in the form of frustum is $V=\frac{1}{3}\pi \left[{\left(r_1\right)}^2+{\left(r_2\right)}^2+\left(r_1\right)\left(r_2\right)\right]\left(h\right)$, where $\left(r_1\right)=28\mathrm{cm}$ and $\left(r_2\right)=7\mathrm{cm}$ represents the radii and $\left(h\right)=45$ represents the height.

$\begin{array}{rcl}V& =& \frac{1}{3}\pi \left[{\left(28\right)}^2+{\left(7\right)}^2+\left(28\right)\left(7\right)\right]\left(45\right)\\ & =& \frac{1}{3}\pi \left[784+49+196\right]45\\ & =& 15435\pi \\ & =& 15435\times 3.142\\ & =& 48486.77{\mathrm{cm}}^3\end{array}$

Therefore, the volume/capacity of the bucket is $\begin{array}{rcl}& & 48486.77{\mathrm{cm}}^3\end{array}$.