Question

the volume of the sphere is $\frac{500}{3}pi$ cubic units. what is the value of x? o 4 units o 5 units o 8 units o 10 units

Explanation:

Step1: Recall volume formula

The volume formula for a sphere is $V = \frac{4}{3}\pi r^{3}$, where $V$ is the volume and $r$ is the radius. Here $r = x$ and $V=\frac{500}{3}\pi$.

Step2: Set up the equation

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

Step3: Eliminate common factors

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

Step4: Solve for $x^{3}$

Divide both sides by 4: $x^{3}=\frac{500}{4}=125$.

Step5: Find $x$

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

Answer:

B. 5 units