PLEASE HELP 15 POINTS 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. 3 6 9 27 81

Accepted Solution

Answer:27Step-by-step explanation:We figure out the scale factor first, which is the number of times one radius is of the other.  We call the scale factor, k.To get how many times larger is the volume of similar spheres, we will need to cube the scale factor.Since it is given that radius of Sphere A is 3 times that of Sphere B, we can say that the scale factor (k) = 3. Hence, the volume of Sphere A would be k^3 times the volume of Sphere B.So,  [tex]k^3\\=(3)^3\\=27[/tex]Hence, the volume of sphere A is 27 times the volume of sphere B.