The radius and height of a right circular cone are in the ratio 3:7. If the volume of the cone is 528 \text{ cm}^3, then what is the height of the cone? (Take \pi=\frac{22}{7})

Explanation

Let radius = 3k and height = 7k. Volume V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \times \frac{22}{7} \times (3k)^2 \times (7k) = 66k^3 = 528. This gives k^3 = 8 \implies k=2. The height is 7(2) = 14 cm.

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