The curved surface area of a cylindrical pillar is 264 m
Question:

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. Find the diameter and the height of the pillar.

Solution:

Here, r  m= radius of the cylinder

m= height of the cylinder

Curved surface area of the cylinder = 2πrh     … (1)

Volume of the cylinder = πr2h                        … (2)

924 = πr2h

$h=\frac{924}{\pi r^{2}}$

Then, substitute h into equation (1):

264 = 2πrh

$264=2 \pi r\left(\frac{924}{\pi r^{2}}\right)$

264r = 2(924)

$r=\frac{2 \times 924}{264}$

r = 7 m, so d = 14 m

$h=\frac{924}{\pi r^{2}}$

$h=\frac{924}{\frac{22}{7} \times 7^{2}}=6 \mathrm{~m}$

Hence, the diameter and the height of the cylinder are 14 m and 6 m, respectively.