SOLUTION: The surface area of a sphere varies directly with the square of its radius. If the surface area of a sphere with a radius of 12 inches if 576 square inches, find the surface area o

Question 103758: The surface area of a sphere varies directly with the square of its radius. If the surface area of a sphere with a radius of 12 inches if 576 square inches, find the surface area of a sphere with a radius of 3 inches
Found 2 solutions by scott8148, Earlsdon:
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
the radius of the smaller sphere is 3/12 or 1/4 of the larger sphere

the surface area is (1/4)^2 or 1/16 ... 576(1/16)=36
Answer by Earlsdon(6294) (Show Source): You can put this solution on YOUR website!
From the problem you can write:
Where S = surface area and k = the proportionality constant.
If S = 576 when r = 12, then we can find the value of k.

Divide both sides by 144.

so...

Now, when r = 3 you can find S.

sq.in.
In reality, the surface area of a sphere is given by:
so the surface area of a shere whose radius is 12 in. would be:

sq.in.
And, if the radius of the sphere is 3 in.. then:

sq.in.
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