Question

the volume of this cone is 2,929.9968 cubic centimeters. what is the radius of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. image of cone with height 24 cm r ≈ □ centimeters submit

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 \( V = 2929.9968\) cubic centimeters, \( h=24\) cm, and \( \pi\approx3.14 \). We need to solve for \( r \).

First, substitute the known values into the formula:
\( 2929.9968=\frac{1}{3}\times3.14\times r^{2}\times24 \)

Step2: Simplify the right - hand side of the equation

Simplify \( \frac{1}{3}\times3.14\times24 \).
\( \frac{1}{3}\times24 = 8 \), so \( \frac{1}{3}\times3.14\times24=3.14\times8 = 25.12 \)
The equation becomes \( 2929.9968 = 25.12r^{2} \)

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

Divide both sides of the equation by \( 25.12 \):
\( r^{2}=\frac{2929.9968}{25.12} \)
\( \frac{2929.9968}{25.12}=116.64 \)
So \( r^{2}=116.64 \)

Step4: Solve for \( r \)

Take the square root of both sides. Since \( r \) represents the radius (a non - negative quantity), we have:
\( r=\sqrt{116.64} \)
\( \sqrt{116.64}=10.8 \)

Answer:

\( 10.8 \)