Question

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

Explanation:

Step1: Recall volume formula for sphere

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

Step2: Set up the equation

Substitute the values into the formula: $\frac{4}{3}\pi x^{3}=\frac{500}{3}\pi$.

Step3: Solve for $x^{3}$

First, cancel out the $\frac{\pi}{3}$ on both sides of the equation. We get $4x^{3}=500$. Then, divide both sides by 4: $x^{3}=\frac{500}{4}=125$.

Step4: Find the value of $x$

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

Answer:

B. 5 units