The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3.
Question:

The curved surface area of a cylindrical pillar is 264 m2 and its volume is 924 m3. The height of the pillar is
(a) 4 m
(b) 5 m
(c) 6 m
(d) 7 m

Solution:

(c)  6 m

Curved surface area $=264 \mathrm{~m}^{2}$

Volume = 924 m3
Let r m be the radius and h m be the height of the cylinder.
Then we have:

$2 \pi r h=264$ and $\pi r^{2} h=924$

$\Rightarrow r h=\frac{264}{2 \pi}$

$\Rightarrow h=\frac{264}{2 r \times \pi}$

Now, $\pi r^{2} h=\pi \times r^{2} \times \frac{264}{2 r \times \pi}=924$

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

$\Rightarrow r=7 \mathrm{~m}$

$\therefore h=\frac{264 \times 7}{2 \times 7 \times 22}=6 \mathrm{~m}$