Two equal circles are drawn on a square in such a way that the opposite side of the square forms the diameter of each circle. If the remaining area of the square is 42 cm2, what is the measurement (in cm) of the diameter of each circle?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 14.
According to the figure
Area of the square = 2 × area of semicircle + 42
⇒ (2r)2 = 2 × 1/2 × π × r2 + 42
⇒ 4r2 = 22/7 × r2 + 42
⇒ 4r2 - 22/7r2 = 42
⇒ r2(28 - 22)/7 = 42
⇒ r2 × 6/7 = 42
⇒ r2 = 49
⇒ r = 7
Now, the diameter of the circle = r + r = 2r
Diameter = 2 × 7 = 14 cm