Chapter 11.8, Problem 3GP

To determine

To compute the area of a sector of the circle.

Answer to Problem 3GP

  $67.1$ squareinches.

Explanation of Solution

Given information: Diameter $d=16$ inches. Radius is half of diameter $r=\frac{16}{2}$

  $=8$ inches.

Formula used: Area of sector of circle $a=\pi \times r^2\times \frac{\theta }{360°}$

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

  $=\frac{22}{7}\times 8^2\times \frac{120°}{360°}$

Taken ‘pi’ as $\frac{22}{7}$ . Also $\theta =120°$

  $=\frac{22}{7}\times 8^2\times \frac{120°}{360°}$

Simplifying the expression.

  $=\frac{22}{7}\times 64\times \frac{1}{3}$

On further simplification.

  $=\frac{22\times 64}{21}$

On multiplying numbers in numerator and then this gets divided by denominator.

  $=67.05$

Rounding to the nearest tenth.

  $=67.1$ square inches.