Question

what is the volume of this sphere? round your answer to the nearest hundredth. 2.9 in cubic inches submit

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Substitute the given radius into the formula

Given \( r = 2.9\) inches. Then \( V=\frac{4}{3}\pi(2.9)^{3}\).
First, calculate \( (2.9)^{3}=2.9\times2.9\times2.9 = 24.389\).
Then, \( V=\frac{4}{3}\times\pi\times24.389\).
\( \frac{4}{3}\times24.389 = 32.51866\cdots\).
So \( V = 32.51866\cdots\times\pi\).
Taking \( \pi\approx3.14159\), we have \( V\approx32.51866\times3.14159\).
\( V\approx102.23\) (rounded to the nearest hundredth).

Answer:

\( 102.23\)