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.
- First, we need to find the radius from the diameter. The diameter is given as 8 yards, so the radius \(r\) is:
\[ r = \frac{8}{2} = 4 \text{ yd} \]
- Now, we can plug the values into the volume formula:
\[ 803.84 = \frac{1}{3}\pi (4)^2 h \]
- Simplifying further, we have:
\[ 803.84 = \frac{1}{3}\pi (16) h \]
\[ 803.84 = \frac{16\pi}{3} h \]
- To isolate \(h\), we first multiply both sides by 3:
\[ 3 \times 803.84 = 16\pi h \]
\[ 2411.52 = 16\pi h \]
- Next, divide both sides by \(16\pi\):
\[ h = \frac{2411.52}{16\pi} \]
- 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.