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by pepeprepa » Mon Sep 01, 2008 7:29 am
This one is faster.

Let's say diameter of S is x.
The sides of the square are x.
The diagonal of the square is x*sqrt(2).
And the diameter of T is x*sqrt(2).

So the area of T is pi*(x*sqrt(2)/2)²=pi*x²/2
The area of S is pi*(x/2)²=pi*x²/4

And T/S = 2
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by 4meonly » Mon Sep 01, 2008 9:12 am
Good rule to use here:

the ratio of squares is the same as the ratio of the sides in the power of 2

the ratio of volumes is the same as the ratio of the sides in the power of 3

Here you are to find the second power of the ratios of the diameters (or the sides of right isolescence triagle formed by the side and the diagonal of the square)
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