Question

The area of a circle of radius 1 is T units squared. Use scaling to explain why the area of a circle of radius r is T/p? units squared.

Answer 1

Given a figure with an area A, if we use a scale factor of b on its dimensions, the new area A' will be:

`A^(\prime)=b^2\cdot A`

Now, if we have a unitary circle (radius = 1) of area A, the scale factor to go to a circle of radius r will be r, because 1*r = r. Then, using the equation above:

`A^(\prime)=r^2\cdot A`

Additionally, we know that the area of the unitary circle is:

`A=\pi\text{ units squared}`

Finally, we conclude:

`A^(\prime)=\pi\cdot r^2\text{ units squared}`