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 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 of the base,
- \( h \) is the height.

1. First, we need to find the radius from the diameter:
\[
\text{Diameter} = 10 \text{ meters} \implies r = \frac{\text{Diameter}}{2} = \frac{10}{2} = 5 \text{ meters}
\]

2. Now we substitute the volume and radius into the volume formula. We know that the volume \( V = 225\pi \):
\[
225\pi = \frac{1}{3} \pi (5^2) h
\]
Simplifying this, we get:
\[
225\pi = \frac{1}{3} \pi (25) h
\]
\[
225\pi = \frac{25}{3} \pi h
\]

3. We can cancel \(\pi\) from both sides:
\[
225 = \frac{25}{3} h
\]

4. Next, we multiply both sides by 3 to eliminate the fraction:
\[
675 = 25h
\]

5. Finally, divide both sides by 25 to solve for \( h \):
\[
h = \frac{675}{25} = 27 \text{ meters}
\]

Thus, the height of the cone is \( \boxed{27} \) meters.