MATH SOLVE

3 months ago

Q:
# 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

Accepted Solution

A:

Answer:The area of sector with radius 3 cm and angle at center is [tex]\frac{9\pi }{8}[/tex] cm² Step-by-step explanation:Given as :The radius of circle = 3 cmThe angle at the center of circle = Ф = [tex]\frac{\pi }{4}[/tex] = 45°Now, Area of sector = [tex]\frac{\Pi r^{2}\times \Theta }{360}[/tex]Or, Area of sector = [tex]\frac{\Pi 3^{2}\times \ 45° }{360°}[/tex] Or, Area of sector = [tex]\frac{\Pi 9\times \ 45° }{360°}[/tex] Or, Area of sector = [tex]\frac{\Pi times \ 45° }{40°}[/tex] Or, Area of sector = [tex]\frac{9\pi }{8}[/tex] cm²Hence The area of sector with radius 3 cm and angle at center is [tex]\frac{9\pi }{8}[/tex] cm² Answer