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 the volume formula of a 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. Given \(V=\frac{500}{3}\pi\).

Step2: Substitute the volume into the formula

Substitute \(V = \frac{500}{3}\pi\) into \(V=\frac{4}{3}\pi r^{3}\), we get \(\frac{500}{3}\pi=\frac{4}{3}\pi r^{3}\).

Step3: Solve for \(r\)

First, cancel out \(\frac{\pi}{3}\) on both sides of the equation \(\frac{500}{3}\pi=\frac{4}{3}\pi r^{3}\), we have \(500 = 4r^{3}\). Then \(r^{3}=\frac{500}{4}=125\). Taking the cube - root of both sides, \(r=\sqrt[3]{125}=5\).

Answer:

5 units