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

8yd diameter

1 answer

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:

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

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

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

  1. Simplifying further, we have:

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

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

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

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

\[ 2411.52 = 16\pi h \]

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

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

  1. 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.