2018 · Q87
If the ratio of the circumference of the base of a right circular cone of radius r to its height is 3:1, then what is the area of the curved surface of the cone?
Elementary MathematicsMensuration
- A3πr²
- B2πr²√(4π² + 9)/3
- Cπr²√(π² + 1)/3
- Dπr²√(4π² + 9)/3
Explanation
From 2πr : h = 3 : 1, h = 2πr/3. Slant height l = √(r² + h²) = r√(1 + 4π²/9) = r√(4π² + 9)/3. Curved surface area πrl = πr²√(4π² + 9)/3, option (D).