Question

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

Answer 1

To find the height of the cone, 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, and \( h \) is the height.

1. **Find the radius**: The diameter of the cone is given as 10 meters, so the radius \( r \) is:

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

2. **Use the volume formula**: We know the volume \( V \) is \( 225\pi \) cubic meters. Substitute \( V \) and \( r \) into the volume formula:

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

3. **Simplify**: First, calculate \( 5^2 \):

\[
5^2 = 25
\]

Then substitute it back into the volume equation:

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

4. **Cancel \( \pi \)** from both sides:

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

5. **Multiply both sides by 3** to eliminate the fraction:

\[
675 = 25h
\]

6. **Solve for \( h \)**:

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

Thus, the height of the cone is:

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