Chapter 1.1, Problem 8WE

To determine

To compare:the areas of the red and blue region.

Answer to Problem 8WE

The area of the red region is the same as the area of the blue region. (estimate)

Explanation of Solution

Given information:

Calculation:

When you measure the diameter of the red region, it would be 11, so radius is 5.5.

So, area of the red region would be

  $\begin{array}{c}A=\pi r^2\\ =\pi \times {\left(5.5\right)}^2\\ =30.25\pi \end{array}$

Area of the blue region:

Diameter of the whole circle is 18.5, so radius would be 9.25.

  $\begin{array}{c}A=\pi r^2\\ =\pi \times {\left(9.25\right)}^2\\ =85.5625\pi \end{array}$

Diameter of the inner circle is 15, so radius is 75

  $A=5.25\pi$

Final area $\begin{array}{l}=85.5625\pi -56.25\pi \\ =29.125\pi \end{array}$

The area of the red region is the same as the area of the blue region. (estimate)