Chapter 11.8, Problem 2GP

To determine

To compute area of the face-off circle that is not red.

Answer to Problem 2GP

  $704$ squarefeet.

Explanation of Solution

Given information: Diameter of face-off circle $=30$ feet or, radius $R=15$ feet. Diameter of circular red spot $=2$ feet or, radius $r=1$ feat.

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

Calculation: To calculate the area of the face-off circle that is not red, subtract the area of the face-off circle‘A’ with the area of the red spot‘a’.

  $A-a=\pi \times R^2-\pi \times r^2$

This can be simplified as

  $=\pi \left(R^2-r^2\right)$

Replacing with the numeric values.

  $=\frac{22}{7}\times \left({15}^2-1^2\right)$

Taken ‘pi’ as $\frac{22}{7}$ .

  $=\frac{22}{7}\times \left(225-1\right)$

On further simplification.

  $=\frac{22}{7}\times 224$

Divide 224 by 7.

  $=22\times 32$

Multiplying the numbers.

  $=704$ square feet.