A right circular cylinder has height $10$ cm. If its total surface area equals its volume, find the radius $r$ of the cylinder. (Use $\pi =\frac{22}{7}$).

Step-by-step solution

1. Write the surface area: $S=2\pi r(r+h)=2\frac{22}{7}r(r+10)$.
2. Write the volume: $V=\pi r^{2}h=\frac{22}{7}{r}^2\times 10$.
3. Set $S=V$ and cancel common factors: $2(r+10)=10r$.
4. Solve for $r$: $2r+20=10rimplies20=8rimpliesr=2.5$ cm.

Concept tested: Radius when surface area equals volume for a cylinder

Published 13 October 2026 · How this solution was prepared and checked