Question

An arc of length 15 cm subtends an angle of 45° at the centre of a circle. Find in terms of 𝜋, radius of the circle.

Answer 1

Length of arc = 15cm

𝜃 = angle subtended at centre = 45°

Let radius = r cm

arc length = `theta/360^@`× 2𝜋𝑟

=`45^@/360^@`× 2𝜋𝑟

`45/360`× 2𝜋𝑟 = 15

𝑟 =`(15×360)/(45×2pi)=60/pi`cms

𝑅𝑎𝑑𝑖𝑢𝑠 =`60/pi`cms