Question

a windshield wiper sweeps out a circular sector with radius r inches, and arc length = 1.4 times the radius.Write a SIMPLIFIED EXPRESSION in the box below that represents the area, in square inches, of the sector the wiper sweeps out.

Answer 1

The central angle θ in radians is given by

`\begin{gathered} \theta=\frac{arc\text{ length}}{radius} \\ \text{ Therefore,} \\ \theta=(1.4r)/(r)=1.4 \end{gathered}`

Area A of a sector with a radius r and a central angle θ in radians is given by:

`A=(1)/(2)r^2\theta`

Hence, the area A is:

`\begin{gathered} A=(1)/(2)r^2(1.4) \\ A=0.7r^2 \end{gathered}`

Therefore, the required simplified expression for the area is

A = 0.7r²