Akshay places three identical rings of diameter 21 cm in such a manner that each one touches the other two rings. He observes that there is a space enclosed by the circles. What is the area (in cm²) of this portion? (Take π = )
Note-Rounded off to the nearest 2 decimal places and √3 = 1.732
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 17.70.
The diameter = 21 cm
Radius (r) = 21/2 = 10.5 cm
When three identical circles touch each other, their centers form an equilateral triangle. The side length of this triangle is equal to twice the radius of the circles (2r).
So, each side length = 2 × 10.5 = 21 cm
Area of triangle = (√3/4) × 212 = (1.732/4) × 441 = 190.953 cm2
Each angle of the equilateral triangle is 60°.
The area of a sector with angle θ (in degrees) and radius r = (θ/360) × πr²
Area of one sector = (60/360) × (22/7) × (10.5)2 = 57.75 cm2
Area of three sectors = 3 × 57.75 = 173.25 cm2
Area of the enclosed space = 190.953 - 173.25 = 17.703 cm2 = 17.70 cm2 (approx)
Therefore, the area of this portion is 17.70 cm2.