Volume of a Sphere Math Example 1

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

Example 1

easy
A basketball has a radius of 12 cm. Find its volume. Leave your answer in terms of ฯ€\pi.

Solution

  1. 1
    Step 1: Write the formula: V=43ฯ€r3V = \frac{4}{3}\pi r^3.
  2. 2
    Step 2: Substitute r=12r = 12: V=43ฯ€(12)3=43ฯ€ร—1728V = \frac{4}{3}\pi (12)^3 = \frac{4}{3}\pi \times 1728.
  3. 3
    Step 3: Simplify: 43ร—1728=4ร—576=2304\frac{4}{3} \times 1728 = 4 \times 576 = 2304. So V=2304ฯ€V = 2304\pi cmยณ.

Answer

V=2304ฯ€V = 2304\pi cmยณ.
The sphere formula V=43ฯ€r3V = \frac{4}{3}\pi r^3 involves cubing the radius, so even small changes in radius have a large effect on volume. Be careful to cube the radius (not the diameter) and then multiply by 43ฯ€\frac{4}{3}\pi.

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 2 medium

A sphere has a volume of [formula] cmยณ. Find its radius.

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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