Circle Pattern

Topic:
Circle

Try the analog task first!

This applet is designed to accompany the MARS task "Circle Pattern" at http://map.mathshell.org/tasks.php?unit=HA04&collection=9

Three points can be dragged. Drag them.

Suppose we scale up a rectangle by a factor of 2, so it grows from a 3x5 rectangle into a 6x10 rectangle. By what factor do we scale its area?

Suppose we triple all side lengths of a square, getting a larger square. By what factor do we scale its area?

Suppose we multiply the radius of a circle by 1/4, obtaining a smaller circle. What happens to its area?

Suppose some geometric object has area A. If we scale that object by the factor r, what does its area become?

By what scale factor should we scale the large black circle pattern, if we want it to perfectly cover one of the smaller white circle patterns inside it?

How does the area of one white circle pattern compare to the area of the whole black circle pattern?

How does the total area of both white circle patterns compare to the area of the black circle pattern?

What fraction of the whole circle is white?

What fraction of the whole circle is black?