Question

The radius of a circle of area a and circumference c is doubled. find the new area of the circle in terms of

a.

Answer 1

By definition, the circumference of a circle is:

`c = 2 * pi * r`
The area of a circle is:

`a = pi * r ^ 2`
Where,
r: radius of the circle.
When the radius is double, then the new area is:

`A = \pi*(2r)^2`
Rewriting we have:

`A = 4 * \pi * r ^ 2`
In terms of a we have:

`A = 4 * a`
Answer:
The new area of the circle in terms of a is:

`A = 4 * a`