Mmmm.....this is an interesting question.......I don't really know!!!...let's see what happens.....
Vs = Vc ????
Let's find the length of the side of the cube that will make the volumes equal.....
(4/3)*pi*r3 = s3 take the cube root of both sides.......
r*[(4/3)*pi]1/3 = s
So this is the length of the side of the cube that makes the volumes equal.
Now let's solve for the length of the side of the cube that makes the areas equal.....
As = Ac ????
4*pi*r2 = 6s2 divide by 6 on both sides
(2/3)*pi*r2 = s2 take the square root of both sides
r*[(2/3)*pi]1/2 = s
And that's the length of the side of the cube that makes the areas equal.
But...it appears that we have a contradiction here.......the length of side of the cube that makes the volumes equal isn't the same as the length of the side of the cube that makes the areas equal. And since our cube isn't a "flexible" one, it seems that the answer to the question is........no.....
Anybody else have a different approach???.......there might be a more common sense reasoning....or perhaps I could be incorrect!!
