Question

Find the radius of the right cylinder shown, in which the height of the cylinder is equal to its diameter.

Answer 1

What is S?

Answer 2

Surface area.\[150\pi \]

Answer 3

@studygurl14

Answer 4

\[
S=Ch+2\pi r^2, \text{ where }C\text{ is circumference of circle.}
\\~\\150\pi=(2\pi r)h+2\pi r^2
\\~\\\text{We are given that }h=2r\text{, so}\\150\pi = (2\pi r)(2r)+2\pi r^2\\~\\
150\pi=4\pi r^2+2\pi r^2\\~\\\text{Now combine like terms}\\150\pi=6\pi r^2\\~\\\text{Divide both sides by }6\pi\\\dfrac{150\pi}{6\pi}=r^2\\~\\
25=r^2\\~\\\text{Take square root of both sides}\\
\boxed{r = 5}
\]