A solid sphere and a solid right circular cylinder have the same total surface area. If the radius of the sphere is $7\text{cm}$, find the height of the cylinder. (Take $\pi =\frac{22}{7}$.)

Step-by-step solution

1. Total surface area of the sphere = $4\pi r^2=4\pi \times 7^2=196\pi {\text{cm}}^2$.
2. Let the cylinder have the same radius $r=7\text{cm}$ and height $h$ (to be found).
3. Total surface area of the cylinder = $2\pi r(h+r)$.
4. Substitute $r=7$: ${\text{CSA}}_{cyl}=2\pi \times 7(h+7)=14\pi (h+7)$.
5. Set the two total surface areas equal: $14\pi (h+7)=196\pi$.
6. Cancel $\pi$ and divide by 14: $h+7=14$.
7. Solve for $h$: $h=14-7=7\text{cm}$.

Concept tested: Equality of sphere and cylinder surface areas

Published 20 August 2026 · How this solution was prepared and checked