Question

A spherical glass vessel has a cylindrical neck $8cm$ long, $2cm$ in diameter; the diameter of the spherical part is $8.5cm.$. By measuring the amount of water it holds, a child finds its volume to be $345c{m}^{3}$. Check whether she is correct, taking the above as the inside measurements, and $\mathrm{\pi }=3.14$.

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Solution

GivenFor the cylinder part, Height $\left(h\right)=8cm$ and Radius $\left(R\right)=\frac{2}{2}cm=1cm$For the spherical part, Radius $\left(r\right)=\frac{8.5}{2}=4.25cm$Find outWe have to verify whether the measurements taken by the child are accurateAmount of water it can hold $=$ Total Volume of this vessel$=$ Volume of cylinder $+$Volume of a sphere$={\mathrm{\pi r}}^{2}\mathrm{h}+\frac{4}{3}{\mathrm{\pi R}}^{3}$$=$$8\mathrm{\pi }+102.35\mathrm{\pi }$On considering $\mathrm{\pi }=3.14$$=110.35\mathrm{\pi }$$=346.499c{m}^{3}$Volume measured by child $=345c{m}^{3},$, which is not rightCorrect volume $=346.5c{m}^{3}$Hence, the Correct volume$=346.5c{m}^{3}$

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