Question

Find the diameter of a cylinder with the volume of 90π cm^3 and a height of 10cm

Answer 1

For this case we have that by definition, the volume of a cylinder is given by:

$V = \pi * r ^ 2 * h$

Where:

r: It is the radius of the cylinder

h: It is the height of the cylinder

According to the problem data we have:

$V = 90 \pi \ cm ^ 3\\h = 10 \ cm$

We replace the data:

$90 \pi = \pi * r ^ 2 * 10$

We simplify:

$90 = 10r ^ 2\\r ^ 2 = \frac {90} {10}\\r ^ 2 = 9\\r = \pm \sqrt {9}$

We choose the positive value:

$r = \sqrt {9}\\r = 3$

Thus, the radius of the cylinder is 3 cm. Therefore the diameter is $d = 2 (3) = 6 \ cm$

Answer:

The diameter of the cylinder is $6 \ cm$