Question

If the radius of a circle is increased by x, by what amount is the circumference of the circle increased? A) x. B) 2x. C) 2piex D) x squared.

Answer 1

c) 2 pi x

Explanation:

The circumference is based on the equations:

C = pi * d where d = diameter

We also know that the radius is half of the diameter as its the length of a line from the centre of the circle while the diameter is the length of two opposite points through the centre of the circle.

This tells us that d = 2r

So we can replace the equation for the circumference with:

C = pi * 2r

An increase of x to the radius would thus mean that the circumference is increased by 2(pi * x), as 2(pi * (r + x) could be used to find the new value of the circumference, which is the same as:

2(pi * r) + 2(pi * x)

So the answer is 2 pi x