Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B. What is the ratio of the volume of sphere A to sphere B?

8 : 1

Step-by-step explanation:

From the above question, we are given the following parameters

Sphere A has a diameter of 6 and is dilated by a scale factor of 2 to create sphere B.

Volume of a sphere = 4/3πr³

For Sphere A , diameter = 6

Radius = Diameter ÷ 2 = 6÷ 2 = 3

Volume of Sphere A = 4/3 × π × 3³

= 113.09733553 cubic units

Approximately = 113.1 cubic units

We were given a scale factor (k) of 2

Because we are dealing with volume, the scale factor will be cubed

In order to find the Volume of the sphere B

k³ = Volume of Sphere A/ Volume of Sphere B

2³ = 113.1 / Volume of Sphere B

Volume of Sphere B = 113.1/ 2³

= 14.1375 cubic units.

The ration of the Volume of Sphere A to Sphere B

Sphere A: Sphere B

113.1 : 14.14

= 8: 1

rounding to the nearest thousandth would be 452,000