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
The curved surface area of a cylindrical pillar

$=2 \pi r h$

Therefore, $2 \pi r h=264$

Volume of a cylinder $=\pi r^{2} h$

Therefore, $\pi r^{2} h=924$

Hence,

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

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

$\Rightarrow r=\left(\frac{924 \times 2}{264}\right)$

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

Therefore,

$2 \pi r h=264$

$\Rightarrow 2 \times \frac{22}{7} \times 7 \times h=264$

$\Rightarrow h=\frac{264}{44}$

$\Rightarrow h=6 \mathrm{~m}$

Hence, the height of the pillar is 6 m.

 

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