Four identical coins are placed in a square. For each coin the ratio of area to circumference is same as the ratio of circumference to area. Then find the area of the square that is not covered by the coins.

Solution

$$\frac{(\pi r^2)}{2 \pi r}$$ = $$\frac{2 \pi r}{ \pi r^2}$$
So r = 2
Hence required area = (Area of square) - (Area of 4 circles)
= $$(8^2) - (4 \pi (2^2))$$ (As side of square will be 4*2 = 8)
= $$16 (4- \pi)$$

The intended diagram can be drawn as follows:

ABCD is the square and the coins are placed (numbered 1,2,3,4)

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CAT 1998 Question Paper Question 60

Four identical coins are placed in a square. For each coin the ratio of area to circumference is same as the ratio of circumference to area. Then find the area of the square that is not covered by the coins.

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