QuestionFour identical coins, each of radius (x + 1) cm, are placed on a table such that each coin touches two others and their centers lie at the vertices of a square. Find the area of the unoccupied region between the coins.
wrong question multiple answers possible.
Reason Given radius of each coin:r = x+1 The centres of the coins form a square.Hence, side of square:= (x+1) + (x+1)= 2x+2Area of square:= (2x+2)^2Inside the square, four quarter circles are present.Since: 4×1/4=1their total area equals one complete circle of radius (x+1).Thus, removed area:= π(x+1) ^2Required unoccupied area:= (2x+2)^2 − π(x+1)2This expression itself matches Option 4 directly.Further simplifying:= 4(x+1)^2 − π(x+1)^2= (x+1)^2 * (4−π) Given π=3.14,= (x^2 + 2x + 1) * (4−3.14) which matches Option 1.Also,(x + 1)^2 * (1−π/4)×4= (x+1)^2 * (4−π) which matches Option 3.
Thus, Options 1, 3, and 4 are mathematically equivalent and produce the same final answer. Hence, the question contains more than one correct option.
