Answer:
A) 10 cm
Step-by-step explanation:
You don't need the Pythagorean Theorem. You can simply use the formula for the volume of a cylinder and solve for the height:
[tex]V=\pi r^2h\\\\90\pi=\pi (3)^2h\\\\90\pi=9\pi h\\\\10=h[/tex]
Therefore, the height of the cylinder is 10 cm.
[tex]\\ \tt\hookrightarrow V=\pi r^2h[/tex]
[tex]\\ \tt\hookrightarrow 3^2\pi h=90\pi[/tex]
[tex]\\ \tt\hookrightarrow \pi h=10\pi[/tex]
[tex]\\ \tt\hookrightarrow h=10cm[/tex]
