Question

Find the height of a cone that has a volume of 225π
225
𝜋
cubic meters and a diameter of 10 meters.(1 point)
The height of the cone is meters.

Answer 1

To find the height of a cone given its volume and diameter, we can use the formula for the volume of a cone:

\[
V = \frac{1}{3} \pi r^2 h
\]

Where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height.

Given:
- The volume \( V = 225\pi \) cubic meters,
- The diameter is 10 meters, so the radius \( r \) is half of the diameter:

\[
r = \frac{10}{2} = 5 \text{ meters}
\]

Now, we can substitute \( V \) and \( r \) into the volume formula and solve for \( h \):

\[
225\pi = \frac{1}{3} \pi (5^2) h
\]

This simplifies to:

\[
225\pi = \frac{1}{3} \pi (25) h
\]

By cancelling \( \pi \) from both sides, we get:

\[
225 = \frac{25}{3} h
\]

Now, multiply both sides by 3 to eliminate the fraction:

\[
675 = 25h
\]

Now, divide both sides by 25 to solve for \( h \):

\[
h = \frac{675}{25} = 27
\]

Thus, the height of the cone is:

\[
\boxed{27} \text{ meters}
\]