Answer:
Step-by-step explanation:
Given that
The area of circle is 25π square unit
Area = 25π square unit
The area of a circle can be calculated using
Area = πr²
Where r is radius of the circle
Then, let find the radius of the circle
Area = πr²
25π = πr²
Divided Both side by π
25π / π = πr² / π
25 = r²
Take square root of both sides
√25 = √r²
5 = r
Then, the radius of the circle is 5 unit
Then, given that the angle subtended by the sector is 9π/10 rad
θ = 9π/10 rad
Then, we want to find the area of the sector
Area of a sector is calculated using
Area of sector = (θ / 360) × πr²
Area of sector = θ × πr² / 360
The formula is in degree let convert to radian
360° = 2π rad.
Then,
Area of sector = θ × πr² / 2π rad
Then,
Area of sector = θ × r² / 2
Area of sector = ½ θ•r²
Then, Area of the sector is
A = ½ θ•r²
A = ½ × (9π / 10) × 5²
A = (9π × 5²) / (2 × 10)
A = 225π / 20
A = 45π / 4
A = 11.25π Square unit
A = 35.34 square unit
