Question

what is the volume of this sphere? round your answer to the nearest hundredth. 10.5 yd cubic yards

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: Identify the radius

Given that the radius \( r = 10.5\) yd.

Step3: Calculate \( r^{3} \)

\( r^{3}=(10.5)^{3}=10.5\times10.5\times10.5 = 1157.625\)

Step4: Substitute into the formula

\( V=\frac{4}{3}\times\pi\times1157.625\)
First, calculate \(\frac{4}{3}\times1157.625\): \(\frac{4\times1157.625}{3}=4\times385.875 = 1543.5\)
Then, \( V = 1543.5\times\pi\)
Using \(\pi\approx3.14159\), \( V=1543.5\times3.14159\approx4849.05\)

Answer:

\(4849.05\)