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

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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) About Me  (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) About Me  (Show Source):
You can put this solution on YOUR website!
From the problem you can write:
S+=+kr%5E2 Where S = surface area and k = the proportionality constant.
If S = 576 when r = 12, then we can find the value of k.
576+=+k%2812%29%5E2
576+=+9%28144%29 Divide both sides by 144.
576%2F144+=+k
k+=+4 so...
S+=+4r%5E2
Now, when r = 3 you can find S.
S+=+4%283%29%5E2
S+=+4%289%29
S+=+36 sq.in.
In reality, the surface area of a sphere is given by:
S+=+4%28pi%29r%5E2 so the surface area of a shere whose radius is 12 in. would be:
S+=+4%28pi%29%2812%29%5E2
S+=+4%28pi%29%28144%29
S+=+576%28pi%29 sq.in.
And, if the radius of the sphere is 3 in.. then:
S+=+4%28pi%29%283%29%5E2
S+=+4%28pi%29%289%29
S+=+36%28pi%29 sq.in.