Question

if the radius of a circle is increased by 50 perent what will be the percent increase in the circumfrence

Answer 1

50%

Explanation:

The equation for circumference is:

`C=2\pi r`

In this case, the radius and the circumference are directly proportional meaning that if the radius increases by 50%, the circumference will also increase by 50%.

Let's use some examples to prove this:

Radius : 2

Increase by 50% : 2*50%=2*(50/100)=2(1/2)=1 --> 1+2 = 3

`C=2\pi r=2\pi 3=6\rightarrow 50 \ percent\ increase\ from\ 4\\C=2\pi r=2\pi 2=4`

Radius : 4

Increase by 50% : 4*50%=4*(50/100)=4(1/2)=2 --> 2+4 = 6

`C=2\pi r=2\pi 6=12\pi\rightarrow50\ percent\ increase\ from\ 8\\C=2\pi r=2\pi 4=8\pi`

In both cases, when we increased the radius by 50%, the circumference also increased by 50%, proving our previous statement correct.

Therefore, when the radius of a circle is increased by 50%, the circumference will also increase by 50%