Chapter 11, Problem 4E

To determine

To calculate the area of sector of the circle.

Answer to Problem 4E

  $34.54$ square inches.

Explanation of Solution

Given information:

Circle has a diameter $d=12$ inches. Hence radius $r=\frac{d}{2}$

  $=\frac{12}{2}$

  $=6$ inches.

Sector of the circle with central angle $\theta =110°$

Formula used:

Area of sector of circle $a=\pi \times r^2\times \frac{\theta °}{360°}$ where ‘r’ is the radius and $\theta$ is the central angle of the sector.

For calculations, $\pi =3.14$ has been used.

Calculation:

Area of the sector of the circle.

  $a=\pi \times r^2\times \frac{\theta °}{360°}$

Formula of sector of circle.

  $=3.14\times 6^2\times \frac{110°}{360°}$

Dividing both the angles by 10.

  $=3.14\times 36\times \frac{11}{36}$

Dividing numerator and denominator by 36.

  $=3.14\times 11$

Multiplying the expression.

  $=34.54$ square inches.