Question

question 6 of 21
what is the volume of the sphere shown?
sphere image
a. $\frac{676}{3}pi$ units³
b. $104pi$ units³
c. $\frac{6788}{3}pi$ units³
d. $52pi$ units³

Explanation:

Step1: Recall the formula for the volume of a sphere

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

Step2: Identify the radius of the sphere

From the diagram, the radius \( r = 13 \) units.

Step3: Substitute the radius into the formula

Substitute \( r = 13 \) into the formula \( V=\frac{4}{3}\pi r^{3} \):
\[

$$\begin{align*} V&=\frac{4}{3}\pi(13)^{3}\\ &=\frac{4}{3}\pi\times2197\\ &=\frac{8788}{3}\pi \end{align*}$$

\]

Answer:

C. \(\frac{8788}{3}\pi\) units\(^3\)