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

If you need immediate math help from PAID TUTORS right now, click here. (paid link)
Click here to see ALL problems on Money Word Problems

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(5891) (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(6103) (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.