Question

A spherical glass vessel has a cylindrical neck $8cm$ long $2cm$ in diameter, the diameter of a 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 $\pi =3.14$

Answer 1

Diameter of spherical glass vessel = 8.5 cm
$\therefore r=4.25$ cm
Length of cylindrical neck = 8 cm
Diameter = 2 cm
$\therefore$ Radius, r = 1 cm
Volume of water she found = 345 cm${}^3$
(i) Volume of cylinder neck, V
$=\pi r^{2}h$
$=\pi \times (1{)}^2\times 8$
$=8\pi c{m}^3$
(ii) Volume of cylindrical vessel $=\frac{4}{3}\pi r^3$
$=\frac{4}{3}\times \pi \times (4.25{)}^3$
$\therefore$ Total volume of water, V
$=8\pi +\frac{4}{3}\pi \times (4.25{)}^3$
$=8\times 3.14+\frac{4}{3}\times 3.14\times (4.25{)}^3$
$=25.12+321.38$
$=346.5c{m}^3$
$\therefore$ Her answer is not correct.