A standard soccer ball subtends an angle of 1 arcminute at a distance of approximately 775 metres. What might the radius of the ball be?
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It has given that a standard soccer ball subtends an angle of 1 arcminute at a distance of approximately 775 m.
we have to find the radius of the ball.
1arcminute = (1/60)°
relation between degree and radian is given by, 1° = π/180 rad
so, (1/60)° = π/180 × 1/60 = π/(10800) rad
now using formula , θ = 2r/D [ see figure ]
r = Dθ/2
= 775 × π/(2 × 10800)
= 775π/21600
≈ 0.11 m = 11cm
therefore, radius of ball might be 11 cm and diameter of ball might be 22cm.
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