Question

Explain how the diagram can help find the area of a circle

Answer 1

Answer:

Step-by-step explanation:

This is a really famous diagram!  The circle has been divided into many wedges (think slices of pizza!).  The wedges have been colored alternately blue and yellow, then the wedges were rearranged to form a "rectangle" -- well, it's approximately a rectangle because the wedges have arcs (pieces of a circle) on them.  See how the bottom and top edges of the rectangle look bumpy?

The area of the "rectangle" is approximately $\pi r^2$ .  The reason is that the height of the rectangle is  r , the radius of the circle.  And the length of the rectangle is about $\pi r$ -- half the circumference of the circle.  It's half because the circumference is in the bumpy parts of the wedges--half blue, half yellow.

The approximation improves as the number of wedges increases.  In fact, as the number of slices (sorry, pizza again) gets larger, the length of the rectangle gets closer and closer to half the circumference.  In other words, making more wedges makes the rectangle less bumpy!