A solid right circular cylinder and a solid sphere have the same total surface area. The cylinder has radius $5\text{cm}$ and unknown height. The sphere has radius $7\text{cm}$. Find the height of the cylinder. Take $\pi =\frac{22}{7}$ and give the answer to one decimal place.

Step-by-step solution

1. Write the total surface area of a cylinder: $2\pi r(h+r)$.
2. Write the total surface area of a sphere: $4\pi R^2$.
3. Set the two areas equal because they are given to be the same.
4. Substitute $r=5$, $R=7$: $2\pi \times 5(h+5)=4\pi \times 7^2$.
5. Calculate the right-hand side: $4\pi \times 49=196\pi$.
6. Cancel the common factor $2\pi$ from both sides: $5(h+5)=98$.
7. Divide by 5: $h+5=19.6$.
8. Subtract 5: $h=14.6\text{cm}$.
9. Hence the required height is $14.6\text{cm}$.

Concept tested: Equality of cylinder and sphere surface areas

Published 28 September 2026 · How this solution was prepared and checked

Related questions

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