Question

what is the volume of this sphere? round your answer to the nearest hundredth. 13 in blank 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 \( r = 13\) inches. Then \( V=\frac{4}{3}\pi(13)^{3}\).
First, calculate \(13^{3}=13\times13\times13 = 2197\).
So \( V=\frac{4}{3}\pi\times2197\).
\( V=\frac{8788\pi}{3}\).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159\), then \( V=\frac{8788\times3.14159}{3}\).
\(8788\times3.14159 = 8788\times(3 + 0.14159)=8788\times3+8788\times0.14159=26364+1244.51292 = 27608.51292\).
\(V=\frac{27608.51292}{3}=9202.83764\approx9202.84\) (rounded to the nearest hundredth).

Answer:

\(9202.84\)