Question

what is the volume of this cone? use π ≈ 3.14 and round your answer to the nearest hundredth. 71 yd (height), 96 yd (diameter) blank cubic yards submit

Explanation:

Step1: Find the radius of the cone

The diameter of the base of the cone is 96 yd, so the radius \( r=\frac{96}{2} = 48 \) yd.

Step2: 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. Here, \( r = 48 \) yd and \( h=71 \) yd, and \( \pi\approx3.14 \).

Step3: Substitute the values into the formula

First, calculate \( r^{2}=(48)^{2}=2304 \). Then, \( \pi r^{2}h\approx3.14\times2304\times71 \). Let's compute that: \( 3.14\times2304 = 7234.56 \), and \( 7234.56\times71=513653.76 \). Then, \( V=\frac{1}{3}\times513653.76 \).

Step4: Calculate the volume

\( \frac{1}{3}\times513653.76 = 171217.92 \)

Answer:

171217.92