Question

A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best describes the change in the radius of the original circle?

Answer 1

Area of a circle is directly proportional to the square of radius of the circle while the circumference is proportional to the radius of the circle. This means that if the radius of a circle is increased x times, then its area will be increased to x^2 times the original area, and the circumference will increase to x times the original circumference.

Thus when the radius is doubled, or in other words if radius mad 2 time the original radius, the area of circle will become 2^2 = 4 time the original area. The circumference will become 2 times the original circumference.

We can calculate exact area and circumference of a circle from its radius using the following equations:

Area of circle = (pi/4)*r^2

Circumference of circle = 2*pi*r

Where r is the radius of the circle.

I know this is a lot, sorry.