Question

what is the volume of this sphere? round your answer to the nearest hundredth. 2.1 yd cubic yards 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 \( r = 2.1\) yd. Then \( V=\frac{4}{3}\pi(2.1)^{3}\).
First, calculate \( (2.1)^{3}=2.1\times2.1\times2.1 = 9.261\).
Then \( V=\frac{4}{3}\pi\times9.261\).
\(\frac{4}{3}\times9.261 = 12.348\).
So \( V = 12.348\pi\).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159\), then \( V=12.348\times3.14159\approx38.79\) (rounded to the nearest hundredth).

Answer:

\(38.79\)