ratio of the area of a circle to its circumference, A/C, is 25/1. what is its circumference?

Question

ratio of the area of a circle to its circumference, A/C, is 25/1. what is its circumference?

Answer 1

Formula for circumference

 

C = 2πr

 

 

Formula for area

 

A = πr²

 

 

where r is radius and π is pi.

 

Now we can set the ratios as equations.

 

A / C = nr² / (2πr)

 

25 / 1 = nr² / (2πr)

 

25 = r / 2

 

 

Multiply both sides of equation by 2.

 

50 = r

 

 

Now plug in this value of r into the formula for circumference.

 

C = 2π(50)

 

C = 100π

Answer 2

Sallie, for this problem try to use the general equations of both.

 

You know that the ratio between the area and circumference is 25/1 so you would say that A/C=25/1 or 25. Knowing the equations of both will help you to cancel out terms that are in both the numerator and denominator. Let's see how this would work:

 

Area of circle (A)= πr²

Circumference of circle (C)= πd or π2r

 

A/C is (πr²)/(π2r) which is the same as...

 

πr²

-----

π2r

 

Expanding out the terms to remove the exponent, the problem becomes...

π•r•r

------

π•2•r

 

showing all the terms, we can remove the terms that appear in both part of the fraction.
π•r•r
------       which leaves r/2

π•2•r

 

Now the problem becomes A/C = r/2= 25. So solve for r by isolating it.

r/2•2= 25•2

r=50

 

Since r=50, use that value for the equation of circumference to find it!

C= π•2•r

C= π•2•50

C= 100π