Volume of a Sphere Math Example 2

Follow the full solution, then compare it with the other examples linked below.

Example 2

medium
A sphere has a volume of 500ฯ€3\frac{500\pi}{3} cmยณ. Find its radius.

Solution

  1. 1
    Step 1: Set up the equation: 43ฯ€r3=500ฯ€3\frac{4}{3}\pi r^3 = \frac{500\pi}{3}.
  2. 2
    Step 2: Multiply both sides by 3ฯ€\frac{3}{\pi}: 4r3=5004r^3 = 500.
  3. 3
    Step 3: Divide by 4: r3=125r^3 = 125.
  4. 4
    Step 4: Take the cube root: r=1253=5r = \sqrt[3]{125} = 5 cm.

Answer

The radius is 55 cm.
To find the radius from the sphere volume, isolate r3r^3 by multiplying by 34ฯ€\frac{3}{4\pi}, then take the cube root. When the volume is given as a multiple of ฯ€\pi, ฯ€\pi cancels neatly. Recognizing perfect cubes (125=53125 = 5^3) allows exact answers.

About Volume of a Sphere

The amount of three-dimensional space inside a sphere, given by 43ฯ€r3\frac{4}{3}\pi r^3.

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More Volume of a Sphere Examples

Example 1 easy

A basketball has a radius of 12 cm. Find its volume. Leave your answer in terms of [formula].

Example 3 easy

A sphere has a diameter of 10 cm. Find its volume. Leave your answer in terms of [formula].

Example 4 hard

If the radius of a sphere is doubled, by what factor does its volume increase? Prove your answer alg

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