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

Answer:

The area of sector with radius 3 cm and angle at center is $\frac{9\pi }{8}$   cm²

Step-by-step explanation:

Given as :

The radius of circle = 3 cm

The angle at the center of circle = Ф = $\frac{\pi }{4}$ = 45°

Now, Area of sector = $\frac{\Pi r^{2}\times \Theta  }{360}$

Or, Area of sector = $\frac{\Pi 3^{2}\times \ 45° }{360°}$

Or, Area of sector = $\frac{\Pi 9\times \ 45° }{360°}$

Or, Area of sector = $\frac{\Pi times \ 45° }{40°}$

Or, Area of sector = $\frac{9\pi }{8}$   cm²

Hence The area of sector with radius 3 cm and angle at center is $\frac{9\pi }{8}$   cm²   Answer