Chapter 11.8, Problem 24PPS

To determine

To compute the area of sector of the circle.

Answer to Problem 24PPS

  $5.3$ squareyards.

Explanation of Solution

Given information: Diameter $d=11$ yards hence radius $r=\frac{11}{2}$ yards.

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

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

Putting the value of the radius.

  $=\frac{22}{7}\times \frac{11}{2}\times \frac{11}{2}\times \frac{20°}{360°}$

Taken $\pi =\frac{22}{7}$ . Also $\theta =20°$

  $=\frac{22}{7}\times \frac{121}{4}\times \frac{1}{18}$

Simplifying the expression.

  $=\frac{2662}{504}$

Dividing the numerator by denominator.

  $=5.28$

Rounding the nearest tenth.

  $=5.3$ square yards.