Question

Mariah made a cylinder out of clay that had a radius of 6 cm and a volume of 72π cm^3. She painted the entire surface of the cylinder purple. How many square centimeters of the cylinder did Mariah paint in terms of π?

Enter the correct answer in the box/blank in terms of π.
_______ cm^2 (squared)

Answer 1

`Answer:\ \boxed{96\pi }\ cm^2`

Explanation:

`R=6\ cm \ \ \ \ V_c=72\pi \ cm^3\ \ \ \ S_c=?`

`V_c=\pi R^2H\\`

`72\pi =\pi 6^2H\\\\72=36H\\`

Divide both parts of the equation by 36:

`2=H\\\\Thus,\ H=2\ cm`

`S_c=2(\pi R^2)+2\pi R(H)\\\\S_c=2\pi (6^2)+2\pi 6(2)\\\\S_c=2\pi(36)+12\pi (2) \\\\S_c=72\pi +24\pi \\\\S_c=96\pi\ cm^2`