What is the perimeter (in cm, rounded off to one decimal place) of the sector of a circle with a radius of 10 cm and an of angle 30°? (Use π = 3.14)
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 25.2.
Perimeter = 2r + arc length
where r is the radius of the circle and
The arc length = θ/360 × 2πr
⇒ 30/360 × 2 × 3.14 × 10
⇒ 1/12 × 2 × 3.14 × 10 = 62.8/12 = 5.23 cm
Now,
Perimeter = 2r + arc length
⇒ 2 × 10 + 5.23
⇒ 20 + 5.23 = 25.23
Thus, the perimeter of the sector is approximately 25.2