Question

Find the area of the sector of a circle of radius 2feet and theta=π/6 radians

Answer 1

Answer:

Given:

Radius =  r = 2 feet

and angle of sector  θ= π/6

Step-by-step explanation:

We need to find Area of sector = A =?

Formula required [ Area of sector =$A=\frac{\theta }{2\pi }\cdot \pi r^2$ ]

so by substitution the given values  in the formula

we get

$A=\frac{\frac{\pi \:}{6\:\:}}{2\pi }\cdot \pi \:2^2\:\\\\ A=\frac{\frac{\pi }{6}\cdot \:2^2}{2} \\\\A=\frac{\frac{2\pi }{3}}{2}\\ \\A=\frac{2\pi }{3\cdot \:2}\\\\ A=\frac{\pi }{3}\\\\ \mathrm{Decimal:\quad }A= 1.04720 \ feet^2$

Hence required area for the sector is 1.0472 feet² or approximately 1.05 feet²