Question

what is the volume of a sphere with a radius of 25.9 in, rounded to the nearest tenth of a cubic inch?

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 \(r = 25.9\) in. Then \(V=\frac{4}{3}\pi(25.9)^{3}\). First, calculate \((25.9)^{3}=25.9\times25.9\times25.9 = 17301.079\).

Step3: Calculate the volume

\(V=\frac{4}{3}\times\pi\times17301.079\). \(\frac{4}{3}\times17301.079 = 23068.1053\). Then \(V=23068.1053\times\pi\approx23068.1053\times3.14159265\approx72433.4\)

Answer:

\(72433.4\) cubic inches