Question

Ramu has a lawn in one corner of his house in the shape shown in the figure (shaded area). The corner of the house is the center of the sector. He has installed a sprinkler system to water his lawn, with the sprinkler head located at the center, instead of using a hose pipe. The central angle of the sector is 216⁰ and the inner and outer radii are 2m and 5m respectively. Find area of the shaded region.

Answer 1

Find area of the outer circle:

Area = πr²

Area = π(5)² = 25π m²

Find area of the outer sector:

Area = 216/360 x 25π = 15π m²

Find area of the inner circle:

Area = πr²

Area = π(2)² = 4π m²

Find area of the inner sector:

Area = 216/360 x 4π = 9π m

Find the area of the shaded region:

Area = 15π - 9π = 6π m² or 18.86 m²

Answer: The area of the shaded region is 18.86 m²