Question : The height of a right circular cone is 24 cm. If the diameter of its base is 36 cm, then what will be the curved surface area of the cone?
Option 1: $1444.6 \; \mathrm{cm^2}$
Option 2: $2400.9\; \mathrm{cm^2}$
Option 3: $1697.14 \; \mathrm{cm^2}$
Option 4: $2144.2\; \mathrm{cm^2}$
Correct Answer: $1697.14 \; \mathrm{cm^2}$
Solution :
Given that the diameter of the base is 36 cm.
So the radius is 18 cm.
Height = 24 cm
$l = \sqrt{r^2 + h^2} = \sqrt{(18)^2 + (24)^2}=30\; \text{cm}$
We know, the curved surface area of a cone
$=\pi rl$, where $r$ = radius and $l$ = slant height
$= \frac{22}{7}\times 18 \times 30=1697.14\; \mathrm{cm^2}$
Hence, the correct answer is $1697.14\; \mathrm{cm^2}$.
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