Question

what is the volume of this cone? round your answer to the nearest hundredth. 8 yd 8 yd ____ cubic yards save answer

Explanation:

Step1: Identify cone dimensions

The cone has a slant height $l=8$ yd and radius $r=8$ yd. First, calculate the height $h$ using the Pythagorean theorem for cones: $h=\sqrt{l^2 - r^2}$.
$h=\sqrt{8^2 - 8^2}=\sqrt{64-64}=0$
Correction: Recognize the diagram labels: the vertical dashed line is height, and the slant side is 8 yd, radius is 8 yd. This is invalid, so assume the vertical line is height $h=8$ yd, radius $r=8$ yd (correct cone structure).

Step2: Use cone volume formula

The volume of a cone is $V=\frac{1}{3}\pi r^2 h$. Substitute $r=8$, $h=8$.
$V=\frac{1}{3}\pi (8)^2 (8)=\frac{1}{3}\pi \times 64 \times 8=\frac{512}{3}\pi$

Step3: Calculate and round

Compute the numerical value: $\frac{512}{3}\pi \approx \frac{512}{3} \times 3.1416 \approx 170.67 \times 3.1416 \approx 536.17$

Answer:

536.17 cubic yards