The figure below shows two circles. The radius of the larger and smaller circle is 4 m and 2 m respectively.Find the area of the shaded area.Pi (π) = 3.14

1. Break Down the Problem

To find the shaded area between the two circles, we need to:

1. Calculate the area of the larger circle.
2. Calculate the area of the smaller circle.
3. Subtract the area of the smaller circle from the area of the larger circle to find the shaded area.

2. Relevant Concepts

The formula for the area $A$ of a circle is: $A = \pi r^2$ where $r$ is the radius of the circle.

3. Analysis and Detail

1. Calculate the area of the larger circle:

   • Radius $r_1 = 4 \, \text{m}$ $A_1 = \pi r_1^2 = 3.14 \times (4)^2 = 3.14 \times 16 = 50.24 \, \text{m}^2$

2. Calculate the area of the smaller circle:

   • Radius $r_2 = 2 \, \text{m}$ $A_2 = \pi r_2^2 = 3.14 \times (2)^2 = 3.14 \times 4 = 12.56 \, \text{m}^2$

3. Calculate the shaded area: $\text{Shaded Area} = A_1 - A_2 = 50.24 \, \text{m}^2 - 12.56 \, \text{m}^2 = 37.68 \, \text{m}^2$

4. Verify and Summarize

We have confirmed the calculations for both circles and can conclude that the shaded area is accurately calculated as well.

Final Answer

The area of the shaded area is $37.68 \, \text{m}^2$.