Question

the volume of a sphere is $\frac{4}{3}\pi r^{3}$. if $r = 3$ cm, what is the volume?
a. $54\pi$ cm$^{3}$
b. $36\pi$ cm$^{3}$
c. $45\pi$ cm$^{3}$
d. $27\pi$ cm$^{3}$

Explanation:

Step1: Substitute \(r = 3\) into the volume formula

The volume formula of a sphere is \(V=\frac{4}{3}\pi r^{3}\). Substitute \(r = 3\) into it, we get \(V=\frac{4}{3}\pi\times(3)^{3}\).

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

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

Step3: Calculate \(\frac{4}{3}\times27\)

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

Answer:

B. \(36\pi\ \text{cm}^3\)