Question

The volume of a cylinder is 54 π cm3. If the radius is 3 cm, what is the height of the cylinder?

An image displaying a cylinder of radius 3 centimetre and volume equals 54 pi cubic centimetre.
A.
18 cm
B.
9 cm
C.
3 cm
D.
6 cm

Answer 1

To find the height of the cylinder, we can use the formula for the volume of a cylinder:

\[
V = \pi r^2 h
\]

where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height.

Given:
- \( V = 54\pi \, \text{cm}^3 \)
- \( r = 3 \, \text{cm} \)

We can substitute the values into the volume formula:

\[
54\pi = \pi (3)^2 h
\]

Simplifying this, we find:

\[
54\pi = \pi (9) h
\]

Now, divide both sides by \( \pi \):

\[
54 = 9h
\]

Next, solve for \( h \):

\[
h = \frac{54}{9} = 6 \, \text{cm}
\]

Therefore, the height of the cylinder is:

\[
\boxed{6 \, \text{cm}}
\]

So the answer is D. 6 cm.