SOLUTION: Sphere A has a diameter that is twice the diameter of sphere B. If 9 gallons of paint are needed to cover the outside of sphere A, how much paint is needed to cover the outside of

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Question 752644: Sphere A has a diameter that is twice the diameter of sphere B. If 9 gallons of paint are needed to cover the outside of sphere A, how much paint is needed to cover the outside of sphere B?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
surface area of a sphere is equal to 4 * pi * r^2

sphere A has a diameter that is 2 times the diameter of sphere B.

this means that sphere A has a radius that is 2 times the radius of sphere B.

if we let the radius of sphere B equal to x, then the radius of sphere A is equal to 2x.

the surface area of sphere A is equal to 4 * pi * (2x)^2 which is equal to 4 * pi * 4x^2 which is equal to 16 * pi * x^2

the surface area of sphere B is equal to 4 * pi * x^2 which is equal to 4 * pi * x^2.

the surface area of sphere A divided by the surface area of sphere B is equal to 16 * pi * x^2 / (4 * pi * x^2 which means that the surface area of sphere A is 4 times the surface area of sphere B.

if it took 9 gallons to cover sphere B, then it will take 36 gallons to cover sphere A.