Question

the volume of this cone is 3,014.4 cubic yards. what is the radius of this cone?
round your answer to the nearest hundredth.
20 yd
r ≈ yards

Explanation:

Step1: Write the formula for the volume of a cone

The volume formula of a cone is \( V=\frac{1}{3}\pi r^{2}h\), where \(V\) is the volume, \(r\) is the radius, and \(h\) is the height. Given \(V = 3014.4\) cubic yards and \(h=20\) yards.

Step2: Substitute the known values into the formula

Substitute \(V = 3014.4\), \(h = 20\) and \(\pi\approx3.14\) into \(V=\frac{1}{3}\pi r^{2}h\). We get \(3014.4=\frac{1}{3}\times3.14\times r^{2}\times20\).
First, simplify the right - hand side: \(\frac{1}{3}\times3.14\times20=\frac{62.8}{3}\). So the equation becomes \(3014.4=\frac{62.8}{3}r^{2}\).

Step3: Solve for \(r^{2}\)

Multiply both sides of the equation by \(3\) to get \(3014.4\times3 = 62.8r^{2}\). Then \(9043.2=62.8r^{2}\).
Divide both sides by \(62.8\): \(r^{2}=\frac{9043.2}{62.8}=144\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\), \(r=\sqrt{144}\).

Answer:

\(12.00\) yards