How to Find the Radius of a Sphere with the Volume

To find the radius of a sphere when you know its volume, you can use the formula for the volume of a sphere, which is:

V = \( \frac{4}{3} \pi r^3 \)

Where:

• V is the volume of the sphere.
• r is the radius of the sphere.
• \( \pi \) is a constant approximately equal to 3.14159.

To isolate the radius (r), you can rearrange the formula. Here are the steps:

1. Start with the volume formula: \( V = \frac{4}{3} \pi r^3 \).
2. Multiply both sides by \( \frac{3}{4} \): \( \frac{3V}{4} = \pi r^3 \).
3. Next, divide both sides by \( \pi \): \( \frac{3V}{4\pi} = r^3 \).
4. Finally, take the cube root of both sides to solve for r: \( r = \sqrt[3]{\frac{3V}{4\pi}} \).

So, if you have the volume of the sphere, plug it into this equation to find the radius.