Question

A conical pit of top diameter$3.5m$ is $12m$ deep. What is its capacity in kiloliters? (Assume$\mathrm{\pi }=22/7$).

Answer 1

Step 1- finding the volume of the pit

Radius of cone $\left(r\right)=3.5/2m$

Height of cone $\left(h\right)=12m$

$$\begin{gathered} Volumeofthecone=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h} \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}\times \frac{22}{7}\times \frac{3.5}{2}\times \frac{3.5}{2}\times 12 \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=38.5m^3 \end{gathered}$$

Step 2 - Finding the capacity of the conical pit.

Now, we know that, $1m^3=1000litre$

$\therefore 38.5m^{3}willcontain=1000\times 38.5=38500litres$

Now, we know that $1000litres=1kilolitre$

So, $38500litres=\frac{38500}{1000}=38.5kilolitres$

Hence, the capacity of the container is $38.5kiloliters$.