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Chapter 10: Problem 55

What happens to the volume of a sphere if its radius is doubled?

Short Answer

Expert verified
When the radius of a sphere is doubled, its volume increases by a factor of 8.

Step by step solution

01

Identify the formula for volume of a sphere

The volume 'V' of a sphere is given by the formula \( V = \frac{4}{3} \pi r^3 \), where 'r' is the radius of the sphere.
02

Apply the change to the formula

For the purpose of this exercise, the radius has been doubled. Hence, instead of 'r', we will now insert '2r' into the formula: \( V' = \frac{4}{3} \pi (2r)^3 \).
03

Simplify the formula

When simplifying \( (2r)^3 \), you'll get \( 8r^3 \). So the new volume becomes \( V' = \frac{4}{3} \pi * 8r^3 \). When simplified further, it becomes \( V' = 8 * \frac{4}{3} \pi r^3 \). As you can see, the new volume is 8 times the original volume.

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