Question : The curved surface area of a right circular cone of diameter $42 \ \text{cm}$ is $990 \ \text{cm}^2$. What is the slant height (in${\ \text{cm}})$ of the cone? [Use $\pi=\frac{22}{7}$]
Option 1: 10
Option 2: 15
Option 3: 24
Option 4: 12
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Correct Answer: 15
Solution :
Diameter = $42 ~cm$
Radius, $r$ = $21 ~cm$
Let $l$ be the slant height.
Curved surface area of a right circular cone = $990 \ \text{cm}^2$
⇒ $\pi r l = 990$
⇒ $\frac{22}{7}×21×l = 990$
⇒ $l$ = $\frac{990}{66} = 15 \ \text{cm}$
Hence, the correct answer is 15 cm.
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