CAT 1998 — QA Question 14
Answer the next 2 questions based on the following information.
A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter ΔABC.
∠BAC = 30°
I(AB) = I(AC) = 10 m
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
- A
16(π - 1)
- B
16(8 - π)
16(4 - π)
- D
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 ).