An arc of length 23.1 cm subtends an 18° angle at the centre. What is the area of the circle? [Use π = 22/7]
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 16978.50 cm2
Given that
An arc of length 23.1 cm subtends an 18° angle at the centre
Formula used
Length of Arc = (θ/360) × 2πr
Area of a Circle = πr2
Calculation
⇒ Length of Arc = (θ/360) × 2πr
⇒ 23.1 = (18/360) × 2πr
⇒ πr = 231
⇒ r = 231 × 7/22 = 147/2 = 73.5 cm
Area of a Circle = πr2
= (22/7) × 73.52 = 16978.50 cm2