Question

question 9 of 10
what is the volume of the sphere below?
a. $\frac{64}{3}\pi$ units$^{3}$
b. $\frac{48}{3}\pi$ units$^{3}$
c. $\frac{256}{3}\pi$ units$^{3}$
d. $\frac{16}{3}\pi$ units$^{3}$

Explanation:

Step1: Recall the volume formula of a sphere

The volume formula of a sphere is \(V = \frac{4}{3}\pi r^{3}\), where \(r\) is the radius of the sphere.

Step2: Identify the radius

From the figure, the radius \(r = 4\).

Step3: Substitute the radius into the formula

Substitute \(r = 4\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(V=\frac{4}{3}\pi\times4^{3}\).

Step4: Calculate \(4^{3}\)

\(4^{3}=4\times4\times4 = 64\).

Step5: Calculate the volume

\(V=\frac{4}{3}\pi\times64=\frac{256}{3}\pi\) units\(^{3}\).

Answer:

C. \(\frac{256}{3}\pi\) units\(^{3}\)