Question

Use the fact that the length of an arc intercepted by an angle is proportional to the radius to find the area of the sector given r = 3 cm and Θ = π 4 . A) 9π 8 cm2 B) 3π 4 cm2 C) 9π 2 cm2 D) 2π 9 cm2

Answer 1

The area of sector with radius 3 cm and angle at center is
`(9\pi )/(8)` cm²

Explanation:

Given as :

The radius of circle = 3 cm

The angle at the center of circle = Ф =
`(\pi )/(4)` = 45°

Now, Area of sector =
`(\Pi r^(2)* \Theta  )/(360)`

Or, Area of sector =
`(\Pi 3^(2)* \ 45° )/(360°)`

Or, Area of sector =
`(\Pi 9* \ 45° )/(360°)`

Or, Area of sector =
`(\Pi times \ 45° )/(40°)`

Or, Area of sector =
`(9\pi )/(8)` cm²

Hence The area of sector with radius 3 cm and angle at center is
`(9\pi )/(8)` cm² Answer