Question

the volume of this cone is 54,174.42 cubic inches. what is the radius of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 71 in cone image r ≈ blank inches

Explanation:

Step1: Recall the volume formula for a cone

The volume \( V \) of a cone is given by the formula \( V=\frac{1}{3}\pi r^{2}h \), where \( r \) is the radius and \( h \) is the height. We know \( V = 54174.42 \) cubic inches, \( \pi\approx3.14 \), and from the diagram, \( h = 71 \) inches. We need to solve for \( r \).

First, substitute the known values into the formula:
\( 54174.42=\frac{1}{3}\times3.14\times r^{2}\times71 \)

Step2: Simplify the right - hand side

First, calculate \( \frac{1}{3}\times3.14\times71 \).
\( \frac{1}{3}\times3.14\times71=\frac{3.14\times71}{3}=\frac{222.94}{3}\approx74.3133 \)
So the equation becomes \( 54174.42 = 74.3133r^{2} \)

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

Divide both sides of the equation by \( 74.3133 \):
\( r^{2}=\frac{54174.42}{74.3133} \)
\( r^{2}\approx729 \)

Step4: Solve for \( r \)

Take the square root of both sides. Since \( r \) represents the radius (a non - negative quantity), we take the positive square root:
\( r=\sqrt{729}=27.00 \) (rounded to the nearest hundredth)

Answer:

\( 27.00 \)