Question

homework d.8.2
score: 2/25 answered: 2/25
question 3
the volume of a cone with height h and radius r can be found using the formula $v = \frac{1}{3}\pi r^{2}h$
sketch a cone with radius 8 feet and height 10 feet, then find the volume.
if needed, round to the nearest tenth.
$\mathrm{ft}^{3}$
question help: video post to forum

Explanation:

Step1: Identify given values

We know that for the cone, the radius \( r = 8 \) feet and the height \( h = 10 \) feet. The formula for the volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \).

Step2: Substitute values into the formula

Substitute \( r = 8 \) and \( h = 10 \) into the formula:
\( V=\frac{1}{3}\pi(8)^{2}(10) \)
First, calculate \( 8^{2}=64 \). Then the expression becomes \( V=\frac{1}{3}\pi\times64\times10 \).
Multiply \( 64\times10 = 640 \), so \( V=\frac{640}{3}\pi \).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( V=\frac{640}{3}\times3.14159 \).
\( \frac{640}{3}\approx213.333 \), then \( 213.333\times3.14159\approx670.206 \). Rounding to the nearest tenth, we get \( V\approx670.2 \).

Answer:

\( 670.2 \)