Question

How does the picture of a circle divided into 8 equal wedges help to explain why the area of the circle is 2πr^2?

Answer 1

The picture of a circle divided into 8 equal wedges helps in understanding the formula for the area of a circle, which is 2πr^2.

Step-by-step explanation:

The picture of a circle divided into 8 equal wedges can help us understand why the area of the circle is 2πr^2.

1. First, we can imagine the circle divided into 360 degrees, with each wedge representing 45 degrees.
2. We know that the total angle around a point is 360 degrees, so the sum of the angles in the wedges must be equal to 360 degrees.
3. Since each wedge represents 45 degrees, there are a total of 360/45 = 8 wedges in the circle.

To find the area of the circle, we can calculate the area of one wedge and then multiply it by the total number of wedges. The area of one wedge is πr^2 * (45/360) = πr^2/8. Multiplying this by 8 gives us the formula for the area of the circle: 2πr^2.

Learn more about Area of a circle