Question

question 5 of 25
what is the volume of the sphere shown below?
a. ( 52pi ) units( ^{3} )
b. ( 104pi ) units( ^{3} )
c. ( \frac{676}{3}pi ) units( ^{3} )
d. ( \frac{8788}{3}pi ) units( ^{3} )

Explanation:

Step1: Recall the formula for the volume of a sphere

The formula for the volume 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 $r = 13$.

Step3: Substitute the radius into the formula

Substitute $r = 13$ into $V=\frac{4}{3}\pi r^{3}$, we get $V=\frac{4}{3}\pi\times13^{3}$.

Step4: Calculate $13^{3}$

$13^{3}=13\times13\times13 = 2197$.

Step5: Calculate the volume

$V=\frac{4}{3}\pi\times2197=\frac{8788}{3}\pi$ units$^{3}$.

Answer:

D. $\frac{8788}{3}\pi$ units$^{3}$