Question

Four circular bangles each of having radius of 6 cm are placed in such a way that each bangle touches two other bangles. The area of the closed space formed by the four bangles is____.

• A. 30.86 cm²
• B. 36 cm²
• C. 40.44 cm²
• D. 28.63 cm²

Hint:

Combine the pipes' combined rate with the partial-fill time to isolate pipe C's rate.

Answer 1

The Correct Option is A

When four identical circles of radius \(r\) are arranged so each one touches two neighbours, their centres form a square with side \(2r\).
The enclosed space in the middle is the area of that square minus the four quarter-circle sectors that together add up to one full circle: Area = \((2r)^2 - \pi r^2\).
Substituting \(r=6\) cm: Area = \(144 - \pi(36) = 144-113.10 = 30.86\) cm², matching option 1.