The sum of the height and the radius of a right circular cylinder is 21 cm, and the radius is less than the height. If the curved surface area of the cylinder is 616 cm^2, then what is the volume of the cylinder? (Take \pi = 22/7)

Explanation

Given h + r = 21 and 2\pi rh = 616. Solving for rh: rh = \frac{616 \times 7}{2 \times 22} = 98. Substituting h = 21 - r yields r(21 - r) = 98 \Rightarrow r^2 - 21r + 98 = 0. The roots are r = 7 or 14. Since r < h, r = 7 cm and h = 14 cm. Volume = \pi r^2h = \frac{22}{7} \times 7^2 \times 14 = 2156 cm^3.

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