There is a fan with 3 blades at 120 to each other whose central circular disc
Answers
Given : There is a fan with 3 blades at 120° to each other whose central circular disc has an area of 3π cm^2 and a blade is (20-√3) cm long.
tips of the blades are joined so as to form an equilateral triangle
To Find : area
(a) 900 cm
(b) 300√3 cm
(c) (900 + 9π) cm^2
(d) (37 + 300 cm^2
Solution:
Area of circular disc = 3π cm²
Area of circle = π(radius)²
=> π(radius)² = 3π
=> radius = √3 cm
Length of fan blade = 20-√3 + √3 = 20 cm
Angle between blades = 120°
Area of one Triangle = (1/2) * 20 * 20 Sin 120°
= 200 (√3 / 2)
= 100 √3
Area of 3 Triangles = 3 * 100 √3 = 300 √3 cm²
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