The radius of a circle of area A and circumference C is doubled.

A)Find the new area of the circle in terms of A .

B)Find the new circumference of the circle in terms of C.

I don’t know how to do this, I’m not used to not having numbers!

### 2 Answers

Hi, CG.

We’ll call the old radius r and the new radius r’ (“r-prime”).

We’re told that the radius is doubled. Thus, r’ = 2r (2 times r).

A) The area of a circle is π × (radius)²

So, the area of the old circle, A = πr²

Use the same formula to get the area of the new circle (let’s call it A’)

A’ = π × (r’)² = π × (2r)² = π × 2² × r² = 4 × πr²

Looking at the expression for A, we can substitute into the expression for A’ and get:

A’ = 4A. Thus the new area of the circle is 4 times the old area.

B) Circumference of a circle is 2π × (radius)

Thus, the old circumference is:

C = 2πr

And the new circumference is:

C’ = 2πr’ = 2π × (2r) = 4πr = 2 × 2πr

Substitute in the equation for C:

C’ = 2C

Thus, the new circumference is 2 times the old circumference

Source(s): Ph.D. in chemical engineeringCircumference equals pi cases the diameter of the circle. subsequently on your question C=10pi centimeters. component of a circle is pi cases the radius squared. subsequently on your question A=25pi sq. centimeters.