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
h 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.