inscribed and circumscribed area question

A circle has a radius of 10 cm. Write a fraction that represents the area of the inscribed square to that of the circumscribed square.
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If the radius of a circle is r then its diameter is 2r, which is also the side of the circumscribed square. Therefore this square has area 4r2. 

Now consider the inscribed square. To find the length of its side we note that the diameter of the circle is a diagonal of the inscribed square. This diagonal is √2 times as long as the side, so, since the diagonal has length 2r, the side of the square is 2r/√2=r√2 and its area is 2r2.

The ratio of the areas of the two squares is 2r2/4r2=½, independent of the length of the radius of the circle. If we put r=10cm, we would have the fraction 200/400=½.

by Top Rated User (1.1m points)

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