Question

A circle has a radius of 11.6 in. If the area is multiplied by 16, what happens to the circumference?

Answer 1

Circumference is times 4

Explanation:

Area is proportional to r²

Area is times 16

Radius is times 4

Since circumference is 2pi×r, it's proportional to r

So circumference is also times 4

Circumference: 2 × pi × (4×11.6)

92.8pi in

Answer 2

It will be 4 times larger

Explanation:

The formula for circumference is

C = 2 * pi *r

The formula for area is

A = pi * r^2

If the area is increased by 16, we will call the new radius b

16A = pi b^2

Divide this equation by the old equation for area

16A = pi b^2

------ -------------

A pi r^2

Canceling

16 = (b/r)^2

Taking the square root of each side

4 = b/r

Multiplying by r on each side

4r = b

The radius increased by 4 times, or the radius is 4 times larger

This will mean that the circumference is 4 times larger