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29 October, 20:30

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?

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  1. 29 October, 20:51
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    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.
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