Question

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

Answer 1

If the radius of a circle of area A and circumference C is doubled, the new circumference of the circle, in terms of C, will be equal to 2C.

The area (A) of a circle is given by:

$A = \pi r^{2}$   (1)

And a circumference (C) is:

$C = 2\pi r$   (2)

Where:

r: is the radius

If the radius of a circle and circumference is doubled, the new circumference of the circle is:

$C_{2} = 2 (2 \pi r) = 2C$

Therefore, the new circumference of the circle in terms of C is equal to 2C.

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