The height of a cylinder is 14 cm and its curved surface area is 264 cm2.

Question:

The height of a cylinder is 14 cm and its curved surface area is 264 cm2. The volume of the cylinder is
(a) 308 cm3
(b) 396 cm3
(c) 1232 cm3
(d) 1848 cm3

Solution:

(b) 396 cm3

Curved surface area of the cylinder $=2 \pi r h=2 \times \frac{22}{7} \times r \times 14$

Therefore,

$2 \times \frac{22}{7} \times r \times 14=264$

$\Rightarrow r=\frac{264}{88}$

$\Rightarrow r=3 \mathrm{~cm}$

Hence, the volume of the cylinder $=\pi r^{2} h$

$=\left(\frac{22}{7} \times 3 \times 3 \times 14\right) \mathrm{cm}^{3}$

$=\frac{2772}{7} \mathrm{~cm}^{3}$

$=396 \mathrm{~cm}^{3}$

 

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