Question

What is the area of the sector with a central angle of 49° and a radius of 11 cm? Use 3.14 for pi and round your final answer to the nearest hundredth

Answer 1

`\boxed{\text{51.71 cm}^(2)}`

Explanation:

If the angle θ is in radians, the formula for the area (A) of a sector of a circle is

A = ½r²θ

If θ is in degrees

`A = (1)/(2)r^(2)\theta * \frac{\pi \text{ rad}}{180^(\circ)}= \pi r^(2)*(\theta )/(360)`

Data:

θ = 49°

r = 11 cm

Calculation:

`\begin{array}{rcl}A& = &3.14* 11^(2)*(49)/(360)\\\\ & = &3.14 * 121 * 0.1361\\ & = & \mathbf{51.71}\\\end{array}\\\text{The area of the sector is }\boxed{\textbf{51.71 cm}^(2)}`