Question

a cone has a volume of 769.3 cubic yards and a height of 15 yards. what is its radius?
round your answer to the nearest hundredth.
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.

Step2: Rearrange the formula to solve for \(r^{2}\)

Given \(V = 769.3\) and \(h=15\), substitute into the formula:

$$
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Step3: Calculate \(r^{2}\)

Take \(\pi\approx3.14\), then \(r^{2}=\frac{769.3}{5\times3.14}=\frac{769.3}{15.7} = 49\)

Step4: Solve for \(r\)

Since \(r^{2}=49\), then \(r=\sqrt{49} = 7.00\) (because radius cannot be negative)

Answer:

\(7.00\)