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 $345{cm}^3$. Check whether she is correct, taking the above as the inside measurement and $\pi =3.16$

Answer 1

We have
Length of the cylindrical neck $h=8cm$
Radius of the cylindrical neck $r=1cm$

Volume of the cylindrical neck
$\Rightarrow \frac{4}{3}\pi \times {\left(\frac{8.5}{2}\right)}^3{cm}^3=\frac{4}{3}\pi \times {\left(4.25\right)}^3{cm}^3$

amount of water in the vessel
$=\{8\pi +\frac{4\pi }{3}\times {\left(4.25\right)}^3\}{cm}^3$

$=3.14\times \{8+\frac{4}{3}\times 4.25\times 4.25\times 4.25\}{cm}^3$

$=346.5{cm}^3$