the volume of the sphere is $\frac{500}{3}pi$ cubic units. what is the value of x? 4 units 5 units 8 units…

Explanation:

Step1: Recall volume formula for sphere

The volume formula of a sphere is $V = \frac{4}{3}\pi r^{3}$. Given $V=\frac{500}{3}\pi$.

Step2: Set up the equation

Set $\frac{4}{3}\pi r^{3}=\frac{500}{3}\pi$.

Step3: Solve for $r^{3}$

Divide both sides of the equation by $\frac{1}{3}\pi$. We get $4r^{3}=500$, then $r^{3}=\frac{500}{4}=125$.

Step4: Solve for $r$

Take the cube - root of both sides. Since $\sqrt[3]{r^{3}}=\sqrt[3]{125}$, then $r = 5$. Here $x$ represents the radius of the sphere.

Answer:

B. 5 units