find the circumference and area using the ratio of the area to the circumfrence

Question

the ratio of the area of the circle to the circumference of the circle a/c is 6/1. find the circumference and area of the circle leave your answer in terms of 

Answer 1

Circumference:  C = 2πr

Area = πr²

 

Your ratio of a:c = 6:1

This means the area is 6 times the circumference...

 

a = 6c

 

πr² = 6(2πr)

πr² = 12πr

 

Divide both sides by πr

πr²/πr = 12πr/πr

r = 12

 

Since we now have the radius we plug that into

the formulas for area and circumference to

finish the problem.

 

a = πr² = π(12²) = 144π

 

c = 2πr = 2π(12) = 24π

 

Answer 2

(pi)r² / 2(pi)r = 6/1  Cross multiply and solve for r

 

(pi)r² = 12(pi)r

 

r = 12