Question

Find the height of a cylinder with a radius of 6 units and a volume of 360π cubic units.
What is the height of this cylinder? Solve on paper and enter your answer on Zearn.
r = 6Area Label Arrow
h = ?
V = 360π
Volume
=
Area of base
⋅
Height
V
=
πr
2

⋅
h


h=

Answer 1

To find the height \( h \) of the cylinder, we can use the formula for the volume of a cylinder:

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

Given:
- Volume \( V = 360\pi \)
- Radius \( r = 6 \)

First, we will calculate the area of the base using the radius:

\[
r^2 = 6^2 = 36
\]

Now, substituting \( r^2 \) back into the volume formula:

\[
V = \pi \cdot 36 \cdot h
\]

We know that the volume \( V \) is \( 360\pi \), so we can set up the equation:

\[
360\pi = \pi \cdot 36 \cdot h
\]

Next, we can divide both sides by \( \pi \) (as long as \( \pi \neq 0 \)) to simplify the equation:

\[
360 = 36h
\]

Now, solve for \( h \) by dividing both sides by 36:

\[
h = \frac{360}{36} = 10
\]

Thus, the height \( h \) of the cylinder is:

\[
\boxed{10} \text{ units}
\]