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 $\mathrm{\pi }=3.14$.

Answer 1

Given

For 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 out

We have to verify whether the measurements taken by the child are accurate

Amount 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 right

Correct volume $=346.5c{m}^3$

Hence, the Correct volume$=346.5c{m}^3$