Question

question 3 of 10
what is the volume of a sphere with a radius of 9 units?

a. ( 972pi ) units( ^ { 3 } )
b. ( 243pi ) units( ^ { 3 } )
c. ( 486pi ) units( ^ { 3 } )
d. ( 324pi ) units( ^ { 3 } )

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.

Step2: Substitute the given radius into the formula

Given \(r = 9\) units. Substitute \(r = 9\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(V=\frac{4}{3}\pi\times9^{3}\).

Step3: Calculate \(9^{3}\)

\(9^{3}=9\times9\times9 = 729\).

Step4: Calculate \(\frac{4}{3}\times729\)

\(\frac{4}{3}\times729=4\times243 = 972\).

Step5: Get the volume

So \(V = 972\pi\) units\(^{3}\).

Answer:

A. \(972\pi\) units\(^{3}\)