In a right circular cylinder, the radius is $r$ cm and the height is $3r$ cm. If the total surface area equals the volume, find the radius $r$. (Use \pi = \frac{22}{7}).

Step-by-step solution

1. Write surface area formula: $S=2\pi r(h+r)$.
2. Substitute $h=3r$: $S=2\pi r(3r+r)=2\pi r\times 4r=8\pi r^2$.
3. Write volume formula: $V=\pi r^{2}h$.
4. Substitute $h=3r$: $V=\pi r^2\times 3r=3\pi r^3$.
5. Set $S=V$: $8\pi r^2=3\pi r^3$.
6. Cancel common factor $\pi r^2$ from both sides: $8=3r$.
7. Solve for $r$: $r=\frac{8}{3}$ cm.

Concept tested: Cylinder SA=volume relationship

Published 16 October 2026 · How this solution was prepared and checked