Q) A circle of diameter 20 cm is equally divided into five sectors. Find the area and perimeter of one of the sectors.

(Q 30 – 30/5/2 – CBSE 2026 Question Paper)

Ans:

Step 1: Given diameter = 20 cm

∴ radius = = 10 cm

Step 2: Since the circle subtends total 360 ⁰ on center and when its divided in 5 sectors,

Then value of angle subtended by each sector = = 72 ⁰

Area of a sector:

Step 3: We know that the area of a sector is given by: π r ² 

from above steps, we have r = 10 cm and θ = 72

∴ Area of a sector = π (10) ² 

= 100 π

= 20 π = 20

= = 62.86 cm ²

Perimeter of a sector:

Step 4: We know that the Perimeter of a sector is given by:

= Arc Length + 2 x Radius

= 2 π r + 2 r

= 2 r (π + 1)

∵ from above steps, we have r = 10 cm and θ = 72 ⁰

∴ Perimeter of a sector = 2 (10)(π +1)

= 20 [ + 1] = 20 [ +1]

= 20 = 4

= = 32.57 cm

Therefore, Area of the sector is 62.86 cm ² and Perimeter of the sector is 32.57 cm

Please press “Heart” if you liked the solution.