A solid cylinder has a radius of \(3 \mathrm{~cm}\) and a total surface area of \(36 \pi \mathrm{cm}^2\). Its height is ____________
Explanation
The total surface area of a solid cylinder is the sum of the curved surface area and the areas of the two circular ends.
T.S.S solid cylinder \(=2 \pi r h+2 \pi r^2\)
\(=2 \pi r(h+r)\)
Here,
\(r=3 \mathrm{~cm}\)
T.S.A solid cylinder \(=36 \pi \mathrm{cm}^2\). Then,
\(36 \pi=2 \pi \times 3(h+3)\)
\(36 \pi=6 \pi(h+3)\)
\(h+3=36 \pi / 6 \pi=6\)
\(h=(6-3) \mathrm{cm}=3 \mathrm{~cm}\)