Question

1. the volume of a sphere is $\frac{4}{3}pi r^{3}$. if $r = 3$ cm, what is the volume?

a. $36pi$ cm$^{3}$
b. $27pi$ cm$^{3}$
c. $54pi$ cm$^{3}$
d. $45pi$ cm$^{3}$

Explanation:

Step1: Substitute the value of \(r\) into the formula

Given the formula \(V=\frac{4}{3}\pi r^{3}\) and \(r = 3\) cm. Substitute \(r\) into the formula: \(V=\frac{4}{3}\pi\times(3)^{3}\)

Step2: Calculate \(3^{3}\)

\(3^{3}=3\times3\times3 = 27\). So the formula becomes \(V=\frac{4}{3}\pi\times27\)

Step3: Simplify the expression

\(\frac{4}{3}\times27=\frac{4\times27}{3}=4\times9 = 36\). So \(V = 36\pi\) \(cm^{3}\)

Answer:

A. \(36\pi\ cm^{3}\)