Question

question 9 of 10
what is the volume of the sphere below?
a. \\(\frac{100}{3}\pi\\) units\\(^3\\)
b. \\(\frac{125}{3}\pi\\) units\\(^3\\)
c. \\(\frac{25}{3}\pi\\) units\\(^3\\)
d. \\(\frac{500}{3}\pi\\) units\\(^3\\)

Explanation:

Step1: Recall sphere volume formula

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

Step2: Identify the radius

From the diagram, the radius $r = 5$.

Step3: Substitute $r=5$ into formula

$$\begin{align*} V &= \frac{4}{3}\pi (5)^3\\ &= \frac{4}{3}\pi \times 125\\ &= \frac{500}{3}\pi \end{align*}$$

Answer:

D. $\frac{500}{3}\pi$ units$^3$