Question

Sphere A has a diameter of 12 and is dilated by a scale factor of one half to create sphere B. What is the ratio of the volume of sphere A to sphere B?

Answer 1

Answer:

VA/VB = 8

Step-by-step explanation:

You have a sphere A with diameter 12, that is, radius 6, which can be written as follow:

$V_A=\frac{4}{3}\pi r_A^3=\frac{4}{3}\pi (6)^3=288\pi$             (1)

The sphere A is dilated by a scale factor of one half to sphere B. Then, you have:

$V_B=\frac{4}{3}\pi r_B^3=\frac{4}{3}\pi (\frac{6}{2})^3=36\pi$       (2)

From the results of equation (2) and (1) you can calculate the ratio VA/VB:

$\frac{V_A}{V_B}=\frac{288\pi}{36\pi}=8$

The ratio of the volumes of both sphere A and B is 8