Question

question
a cone with a height of 15 yards has a volume of 475.17 ( yd^3 ). find the diameter of the cone.

answer attempt 1 out of 2
( r = square )
( d = square )
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Explanation:

Step1: Write the volume formula for a cone

The volume formula for a cone is \( V=\frac{1}{3}\pi r^{2}h\). Given \(V = 475.17\ yd^{3}\) and \(h=15\ yd\).

Step2: Solve for \(r^{2}\)

Substitute the values into the formula: \(475.17=\frac{1}{3}\times\pi\times r^{2}\times15\).
First, simplify \(\frac{1}{3}\times15 = 5\). So the equation becomes \(475.17 = 5\pi r^{2}\).
Then, \(r^{2}=\frac{475.17}{5\pi}\). Taking \(\pi\approx3.14\), we have \(r^{2}=\frac{475.17}{5\times3.14}=\frac{475.17}{15.7}\approx30.2656\).

Step3: Solve for \(r\)

\(r=\sqrt{30.2656}\approx5.5\ yd\).

Step4: Find the diameter \(d\)

Since \(d = 2r\), then \(d=2\times5.5 = 11\ yd\).

Answer:

\(r = 5.5\ yd\), \(d = 11\ yd\)