Question

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?

Answer 1

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.