do not understand

Question

Consider two circles, a smaller one and a larger one. If the larger one has a radius that is 1 feet larger than that of the smaller circle and the ratio of the circumferences is 2:1, what are the radii of the two circles?

Answer 1

If the circumferences are in the ratio of 2:1, then the radii are in ratio of 2:1.

The only numbers that differ by 1 and are in ratio 2:1 are 2 and 1.

Answer 2

Let radius of smaller circle = r

Let radius of larger circle = r + 1

 

Using the circumference formula with their ratio, we can write an equation in terms of r.

 

2π(r + 1) / 2πr = 2 / 1

 

 

Solving for r,

 

(r + 1) / r = 2

 

r + 1 = 2r

 

1 = r

Answer 3

Consider that the circumference of a circle is given by C = 2 Pi*r.

 

the ratio the circumference of circle a divided by the circumference of circle b is 2/1

then:

a/b = 2/1

(2 pi * r_a) / (2 pi * r_b) = 2/1

r_a / r_b = 2

 

We are given that the larger circle has a radius 1 foot longer the the smaller.

we can rewrite the above equation letting r_a = r_b +1.

 

(r_b + 1) / r_b = 2

r_b + 1 = 2 r_b

1 = r_b

 

So the smaller circle has a radius of 1 foot and the larger has a radius of 2 feet.