Question

The volume of a cylinder is 108π cm³ and its height is 12 cm. What is the length of the cylinder's radius? Enter your answer in the box.

Answer 1

Answer:

$\boxed{r=3cm}$

Step-by-step explanation:

The volume of a cylinder is given by the formula;

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

It was given that the volume of the cylinder, $V=108\pi$, and its height, $h=12cm$

We substitute the given values into the formula to obtain;

$108\pi=\pi\times r^2\times 12$

We divide through by $12\pi$ to obtain;

$\frac{108\pi}{12\pi}=r^2$

$\Rightarrow 9=r^2$

We take the positive square root of both sides to obtain;

$\Rightarrow \sqrt{9}=r$

$3=r$

$r=3cm$

Therefore the length of the cylinder's radius is 3cm.

Answer 2

Answer:

the radius is 3 cm

Step-by-step explanation:

The volume of a cylinder is given by

V = pi *r^2 h

We know the volume = 108 *pi  and the height = 12

Substituting into the equation

108 * pi = pi * r^2 * 12

Divide each side by pi

108 * pi/pi = pi/pi * r^2 * 12

108  =   r^2 * 12

Divide each side by 12

108/12 = r^2*12/12

9 = r^2

Take the square root of each side

sqrt(9) = sqrt(r^2)

3 = r