Question:
The curved surface area of cylindrical pillar is $264 \mathrm{~m}^{2}$ and its volume is $924 \mathrm{~m}^{3}$. Find the diameter and the height of the pillar.
Solution:
Let, r be the radius of the cylindrical pillar
h be the height of the cylindrical pillar
$C S A=264 \mathrm{~m}^{2}$
$2 \pi r h=264 m^{2} \ldots .1$
$\Rightarrow$ volume of the cylinder $=924 \mathrm{~m}^{2}$
$\Pi^{*} r^{2} * h=924$
πrh(r) = 924
πrh = 924/r
Substitute πrh in eq 1
2 * 924/r = 264
r = 1848/264
r = 7 m
Substitute r value in eq 1
2 * 22/7 * 7 * h = 264
h = 264/44
h = 6 m
so, the diameter = 2r = 2(7) = 14 m and height = 6 m