Question

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 using the volume formula, we can start with the given formula for the volume \( V \) of a cylinder:

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

You provided the values:
- \( V = 360\pi \)
- \( r = 6 \)

First, we will substitute the known value of \( r \) into the volume formula.

1. Calculate the area of the base using the radius:

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

2. Substitute \( r^2 \) into the volume formula:

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

This simplifies to:

\[
V = 36\pi h
\]

3. Now set this equal to the provided volume:

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

4. To solve for \( h \), divide both sides by \( 36\pi \):

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

The \( \pi \) cancels out:

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

5. Now simplify \( \frac{360}{36} \):

\[
h = 10
\]

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

\[
\boxed{10}
\]