Question
Download Solution PDFThree circles of radius 35 cm are placed in such a way that each circle touches the other two. What will be the area of the portion enclosed by these three circles?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Radius of each circle = 35 cm
Each circle touches the other two (forms an equilateral triangle between centers)
Formula used:
Area enclosed between 3 touching circles = Area of equilateral triangle formed by centers − 3 × Area of sector
Area of equilateral triangle = (√3 / 4) × side2
Area of sector = (60° / 360°) × πr2 = (1/6) × πr2
Calculation:
Side of triangle = 2 × radius = 2 × 35 = 70 cm
Area of triangle = (√3 / 4) × 702 = (√3 / 4) × 4900 = 1225√3 cm2
Area of one sector = (1/6) × (22/7) × 352
= (1/6) × (22/7) × 1225 = 3850 / 6 = 641.67 cm2 (approx)
Total area of 3 sectors = 3 × 641.67 = 1925.01 = 1925 cm2 (approx)
Enclosed area = 1225√3 − 1925 cm2
∴ Required area = 1225√3 − 1925 cm2
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