Question

This cone has a volume of 803.84 yd 3. Find the height of the cone.
8yd diameter

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. First, we need to find the radius from the diameter. The diameter is given as 8 yards, so the radius \(r\) is:

\[
r = \frac{8}{2} = 4 \text{ yd}
\]

2. Now, we can plug the values into the volume formula:

\[
803.84 = \frac{1}{3}\pi (4)^2 h
\]

3. Simplifying further, we have:

\[
803.84 = \frac{1}{3}\pi (16) h
\]

\[
803.84 = \frac{16\pi}{3} h
\]

4. To isolate \(h\), we first multiply both sides by 3:

\[
3 \times 803.84 = 16\pi h
\]

\[
2411.52 = 16\pi h
\]

5. Next, divide both sides by \(16\pi\):

\[
h = \frac{2411.52}{16\pi}
\]

6. Using \(\pi \approx 3.14159\):

\[
h \approx \frac{2411.52}{16 \times 3.14159}
\]

\[
h \approx \frac{2411.52}{50.26544} \approx 48.0 \text{ yd}
\]

The height of the cone is approximately **48.0 yards**.