Question

$3080c{m}^3$ of water is required to fill a cylindrical vessel completely and $2310c{m}^3$ of water is required to fill it up to $5cm$ below the top. Find the height of the vessel in cm.

Answer 1

Volume of cylindrical vessel $=3080c{m}^3$
$V=\pi r^{2}h$
$3080=\pi r^{2}h$
$h=\frac{980}{r^2}$
Volume of same cylindrical vessel of height $(h-5)cm$
$V=\pi r^2(h-5)$
$2310=\pi r^2(\frac{980}{r^2}-5)$
$2310=\pi (980-5r^2)$
$245=5r^2$
$r=7cm$

$\therefore h=\frac{980}{r^2}$$=\frac{980}{49}=20cm$