Honors problem 29

Question

Find the radius of a circle so that it's area and circumference are the same value.

Answer 1

Hi Nick,

 

area = pi x r^2 and circumference = 2pi x r

 

If they are the same value, then pi x r^2 = 2pi x r

 

Divide both sides by r--> pi x r = 2pi

 

Divide both sides by pi --> r = 2

 

Dan

Answer 2

Area of circle = πr² 

Circumference of circle = 2πr

 

As per the question, area = circumference 

 

πr² = 2πr

dividing both sides by πr, 

 

r=2

 

Answer: For radius of a circle being 2 units, area and circumference of the circle are of same value.

Answer 3

Hello,

 

The circumference = 2Πr

The Area = Πr²

 

Now we want to set them equal and solve:

 

2Πr = Πr²

First we can divide each side by pi giving us: 2r = r²

 

Then we can divide both sides by r giving us: 2 = r

 

Hope that helps