Chapter 9.2, Problem 30E

To determine

To find: The error in the given procedure to find the area of the sector with given details.

Answer to Problem 30E

The formula is wrong as the angle should be in radians and the correct area of the sector is $12.56{\text{cm}}^2$ .

Explanation of Solution

Given:

The radius of the sector is 6 cm and the central angle is $40°$ .

The given area of the sector is,

  $\begin{array}{c}A=\frac{1}{2}{\left(6\right)}^2\left(40\right)\\ =720{\text{cm}}^2\end{array}$

Calculation:

Consider thegiven area of the sector is,

  $\begin{array}{c}A=\frac{1}{2}{\left(6\right)}^2\left(40\right)\\ =720{\text{cm}}^2\end{array}$

The above method is wrong as the angle should be in radians.

The correct area of the sector is obtained as,

  $\begin{array}{c}A=\frac{1}{2}{\left(6\right)}^2\left(40°\right)\left(\frac{\pi }{180°}\right)\\ =\frac{1}{2}{\left(6\right)}^2\left(\frac{2\pi }{9}\right)\\ =12.56{\text{cm}}^2\end{array}$