Question

A circular ring of radius 10 inches is reshaped into an arc of a circle of radius 5 feet show that this arc subtends an angle of 60° at the centre

Answer 1

A circular ring of radius 10 inches is reshaped j to an arc of a circle of radius 5 feet.

we know, 1 feet = 12 inches
5 feet = 60 inches.

radius of arc , R = 60 inches.
Let ∅ is the angle subtends at the centre of arc.
then, length of arc = ∅ × R [ because we know, ∅ = arc length/radius ]
length of arc = 60∅ inches.

now, radius of initial circle , r = 10 inches
circumference of circle = 2πr = 2π × 10 inches.
= 20π inches.

now, circumference of circle = length of arc
20π = 60∅
∅ = 20π/60 = π/3 or, 60°

hence , proved