Question : What is the area of the curved surface of a right circular cone with a height of 8 m and a slant height of 10 m?
Option 1: $60\mathrm{~m}^2$
Option 2: $60\pi \mathrm{~m}^2$
Option 3: $40 \mathrm{~m}^2$
Option 4: $ 40 \pi \mathrm{~m}^2$
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Correct Answer: $60\pi \mathrm{~m}^2$
Solution :
Given: Height($h$) = 8 m and slant height($l$) = 10 m
Radius($r$) = $\sqrt{l^2-h^2}$
= $\sqrt{10^2-8^2}$
= $\sqrt{100-64}$
= $\sqrt{36}$
= 6 m
Area of the curved surface of a right circular cone
= $ \pi rl$
= $\pi×6×10$
= $60\pi $
Hence, the correct answer is $60\pi \mathrm{~m}^2$.
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