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, $\pi r^{2} h=\pi \times r^{2} \times \frac{264}{2 r \times \pi}=924$
$\Rightarrow r=\frac{924 \times 2}{264}$
$\Rightarrow r=7 \mathrm{~m}$
$\therefore h=\frac{264 \times 7}{2 \times 7 \times 22}=6 \mathrm{~m}$
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