Question

what is the volume of this sphere? round your answer to the nearest hundredth. 10 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: Identify the radius

Given that the radius \( r = 10\) inches.

Step3: Substitute the radius into the formula

Substitute \( r = 10\) into \( V=\frac{4}{3}\pi r^{3}\). So \( V=\frac{4}{3}\pi(10)^{3}\).
First, calculate \( (10)^{3}=1000\). Then \( V=\frac{4}{3}\pi\times1000=\frac{4000}{3}\pi\).

Step4: Calculate the numerical value

Using \( \pi\approx3.14159\), we have \( V=\frac{4000}{3}\times3.14159\).
\( \frac{4000\times3.14159}{3}=\frac{12566.36}{3}\approx4188.79\)

Answer:

\(4188.79\)