Question

A sphere is dilated by a scale factor of 1.5 to create a new sphere. How does the volume of the new sphere compare with the volume of the original sphere?

Answer 1

Answer:

The volume of new sphere is 3.375 times greater than the volume of old sphere

Step-by-step explanation:

Let r be the radius of old sphere. This old  sphere is dilated by a scale factor of 1.5 to create a new sphere, so the radius of new sphere is R=1.5r.

The volume of the sphere can be calculated using formula

$V=\dfrac{4}{3}\pi r^3$

Hence,

$V_{old}=\dfrac{4}{3}\pi r^3\\ \\V_{new}=\dfrac{4}{3}\pi R^3=\dfrac{4}{3}\pi (1.5r)^3\\ \\\dfrac{V_{new}}{V_{old}}=\dfrac{\dfrac{4}{3}\pi (1.5r)^3}{\dfrac{4}{3}\pi r^3}=1.5^3=3.375$