Question

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

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Solution

## Step 1- finding the volume of the pitRadius of cone $\left(r\right)=3.5/2m$Height of cone $\left(h\right)=12m$$Volumeofthecone=\frac{1}{3}{\mathrm{\pi r}}^{2}\mathrm{h}\phantom{\rule{0ex}{0ex}}\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=\frac{1}{3}×\frac{22}{7}×\frac{3.5}{2}×\frac{3.5}{2}×12\phantom{\rule{0ex}{0ex}}\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{cone}=38.5{m}^{3}$Step 2 - Finding the capacity of the conical pit.Now, we know that, $1{m}^{3}=1000litre$$\therefore 38.5{m}^{3}willcontain=1000×38.5=38500litres$Now, we know that $1000litres=1kilolitre$So, $38500litres=\frac{38500}{1000}=38.5kilolitres$Hence, the capacity of the container is $38.5kiloliters$.

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