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

$\begin{gathered} \theta=\frac{arc\text{ length}}{radius} \\ \text{ Therefore,} \\ \theta=\frac{1.4r}{r}=1.4 \end{gathered}$

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

$A=\frac{1}{2}r^2\theta$

Hence, the area A is:

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

Therefore, the required simplified expression for the area is

A = 0.7r²