Chapter 13.6, Problem 36WE

To determine

To find: the area of the region.

Answer to Problem 36WE

The area of the region is $29.33$ .

Explanation of Solution

Given information: The circle $x^2+y^2=2$ and above the line $y=1$ .

Calculation:

  $\theta =78.5$

Area covered by the sector $=\frac{2\theta }{360}\times \pi r^2$

  $\begin{array}{l}\Rightarrow \frac{2\left(78.5\right)}{360}\times \pi {\left(5\right)}^2\\ \Rightarrow 34.23\end{array}$

Area of triangle $=\frac{1}{2}\times \text{base}\times \text{height}$

  $\begin{array}{l}\Rightarrow \frac{1}{2}\times 1\times 4.9\\ \Rightarrow 2.45\end{array}$

Required area:

  $\begin{array}{l}\Rightarrow 34.23-2.45\times 2\\ \Rightarrow 29.33\end{array}$