Question

what is the volume of this sphere? round your answer to the nearest hundredth. 13 mm cubic millimeters

Explanation:

Step1: Recall volume formula

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $r$ is the radius of the sphere.

Step2: Substitute radius value

Given $r = 13$ mm, we substitute it into the formula: $V=\frac{4}{3}\pi(13)^{3}$.
First, calculate $(13)^{3}=13\times13\times13 = 2197$.
Then, $V=\frac{4}{3}\pi\times2197=\frac{8788\pi}{3}$.

Step3: Calculate the value and round

Using $\pi\approx3.14159$, we have $V=\frac{8788\times3.14159}{3}$.
$8788\times3.14159 = 8788\times(3 + 0.14159)=8788\times3+8788\times0.14159=26364+1244.79792 = 27608.79792$.
$V=\frac{27608.79792}{3}\approx9202.93$ cubic - millimeters.

Answer:

$9202.93$