For this case we have that by definition, the volume of a cylinder is given by:
[tex]V = \pi * r ^ 2 * h[/tex]
Where:
r: It is the radius of the cylinder
h: It is the height of the cylinder
According to the problem data we have:
[tex]V = 90 \pi \ cm ^ 3\\h = 10 \ cm[/tex]
We replace the data:
[tex]90 \pi = \pi * r ^ 2 * 10[/tex]
We simplify:
[tex]90 = 10r ^ 2\\r ^ 2 = \frac {90} {10}\\r ^ 2 = 9\\r = \pm \sqrt {9}[/tex]
We choose the positive value:
[tex]r = \sqrt {9}\\r = 3[/tex]
Thus, the radius of the cylinder is 3 cm. Therefore the diameter is [tex]d = 2 (3) = 6 \ cm[/tex]
Answer:
The diameter of the cylinder is [tex]6 \ cm[/tex]
