CAT 1998 — QA Question 14
Basics of QuadrilateralsEasy
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.
Answer & solution
Correct answer: 16(4 - π)
- A
16(π - 1)
- B
16(8 - π)
16(4 - π)
- D
Solution
Let R be the radius of each circle. Then 2 which implies that i.e., R2 = 4, i.e. R = 2.
Then the length of the square is 8. Thus, the area of the square is 64, while the area covered by each coin is π22 = 4π. Since there are four coins, the area covered by coins is 4(4π ) = 16π.
Hence, the area not covered by the coins is 64 – 16π = 16(4 – π ).