Question

the volume of this cone is 6,443.28 cubic meters. what is the radius of this cone? round your answer to the nearest hundredth. 19 m r ≈ meters submit

Explanation:

Step1: Recall the volume formula of a cone

The volume formula of a cone is \( V=\frac{1}{3}\pi r^{2}h \). Given \( V = 6443.28\space m^{3}\) and \( h=19\space m\), we can rewrite the formula for \( r^{2}\) as \( r^{2}=\frac{3V}{\pi h}\).

Step2: Substitute the values into the formula

Substitute \( V = 6443.28\), \( h = 19\), and \( \pi\approx3.14\) into \( r^{2}=\frac{3V}{\pi h}\).

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Step3: Solve for \( r\)

Since \( r^{2}=324\), then \( r=\sqrt{324} = 18.00\) (because radius \( r>0\)).

Answer:

\(18.00\)