Question 103758
From the problem you can write:
{{{S = kr^2}}} 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(12)^2}}}
{{{576 = 9(144)}}} Divide both sides by 144.
{{{576/144 = k}}}
{{{k = 4}}} so...
{{{S = 4r^2}}}
Now, when r = 3 you can find S.
{{{S = 4(3)^2}}}
{{{S = 4(9)}}}
{{{S = 36}}} sq.in.
In reality, the surface area of a sphere is given by:
{{{S = 4(pi)r^2}}} so the surface area of a shere whose radius is 12 in. would be:
{{{S = 4(pi)(12)^2}}}
{{{S = 4(pi)(144)}}}
{{{S = 576(pi)}}} sq.in.
And, if the radius of the sphere is 3 in.. then:
{{{S = 4(pi)(3)^2}}}
{{{S = 4(pi)(9)}}}
{{{S = 36(pi)}}} sq.in.