Find the area of a sector with the given central angle θ in a circle of radius r.
θ = 90°, r = 6 cm
A = 1/2r^2 θ
A = 1/2(6)^2(pi/2)
A = 1/2(36)(pi/2)
A = 9pi cm^2
To find the area of a sector, you need to use the formula:
Area = (θ/360) * π * r²
Where:
- θ is the central angle of the sector
- r is the radius of the circle
- π is a constant (approximately equal to 3.14159)
In this case, θ is given as 90° and r is given as 6 cm. Let's substitute these values into the formula and calculate the area.
Area = (90/360) * π * 6²
= (1/4) * π * 36
= 9π cm²
So, the area of the sector with a central angle of 90° and a radius of 6 cm is 9π cm².