Question

Sphere A is similar to sphere B. If the radius of sphere A is 3 times the radius of sphere B, then the volume of sphere A is _______ times the volume of sphere B?

1) 1/3
2) 1/9
3) 1/27
4) 1/81

Answer 1

The volume of sphere A is 27 times the volume of sphere B because the radius of sphere A is 3 times the radius of sphere B, and the volume of a sphere scales with the cube of the radius.

Step-by-step explanation:

The question pertains to understanding the relationship between the volumes of similar figures, specifically spheres in this case. When looking at the volumes of spheres, we use the formula V = (4/3)πr³, where V is the volume and r is the radius.

As sphere A has a radius that is 3 times the radius of sphere B, we can represent the radius of sphere A as 3r (if we assume the radius of sphere B is r). Therefore, the volume of sphere A would be VA = (4/3)π(3r)³, which simplifies to VA = (4/3)π27r³ because (3r)³ equals 27r&u00b3.

Comparatively, the volume of sphere B is VB = (4/3)πr³. To find the relationship between VA and VB, we divide VA by VB and find that sphere A's volume is 27 times the volume of sphere B, since 27r³/r³ equals 27.