Chapter 11.8, Problem 20PPS

To determine

To compute the area of the CD.

Answer to Problem 20PPS

  $111.4$ squarecentimeters.

Explanation of Solution

Given information: Diameter of CD $=12$ centimeters or, radius $=6$ centimeters. Diameter of circular hole in the CD $=1.5$ or $\frac{3}{2}$ centimeters or, radius $r=\frac{3}{4}$ centimeters.

Formula used: Area of circle $A=\pi \times r^2$

Calculation: To calculate the area of the CD, subtract the area of the CD‘A’ with the area of the circular hole‘a’.

  $A-a=\pi \times R^2-\pi \times r^2$

On simplifying the same.

  $=\pi \left(R^2-r^2\right)$

Putting the values in the expression.

  $=\frac{22}{7}\times \left(6^2-\frac{3^2}{4^2}\right)$

Taken $\pi =\frac{22}{7}$ .

  $=\frac{22}{7}\times \left(36-\frac{9}{16}\right)$

Simplifying the expression.

  $=\frac{22}{7}\times \frac{567}{16}$

On computing the expression.

  $=111.38$

Rounding to the nearest tenth.

  $=111.4$ square centimeters.