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?

Question

asked Jan 1, 2021 166k views

2 Answers

Millard · Answer 1 · 2021-01-08T07:17:12+0000

Answer:

VA/VB = 8

Explanation:

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

$V_A=(4)/(3)\pi r_A^3=(4)/(3)\pi (6)^3=288\pi$ (1)

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

$V_B=(4)/(3)\pi r_B^3=(4)/(3)\pi ((6)/(2))^3=36\pi$ (2)

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

$(V_A)/(V_B)=(288\pi)/(36\pi)=8$

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