How can I calculate the radius of a sphere if I know its volume?

by

Finding the radius of a sphere when you have its volume is a straightforward process that involves some basic algebra and geometric formulas. The volume V of a sphere is calculated using the formula:

V = (4/3) * π * r³

where r is the radius of the sphere and π (pi) is approximately 3.14159. To find the radius from the volume, you will need to take the following steps:

  1. Start with the volume formula:
    You already have the volume V.
  2. Rearrange the formula to solve for r:
    Begin by isolating r³:
r³ = (3V)/(4π)
  1. Calculate r³:
    Plug your value of V into the equation:
r³ = (3 * volume) / (4 * π)
  1. Take the cube root:
    To find r, take the cube root of r³:
r = ∛((3V)/(4π))

Now, let’s put this into practice with an example. Suppose the volume of a sphere is 113.1 cubic units. To find the radius:

  1. Plug the volume into the equation:
    V = 113.1
  2. Calculate:
    r³ = (3 * 113.1) / (4 * π) ≈ 27.0
  3. Take the cube root:
    r ≈ ∛27.0 = 3

So, the radius of the sphere is approximately 3 units.

By following these steps, you can easily find the radius of a sphere given its volume. This knowledge is not only useful in academic settings but can also come in handy in practical applications such as engineering, architecture, and various fields of science.

Leave a Comment