Question

Circle X has radius r X = 6 units and circumference C X = 12 π units.

Circle Y has circumference C Y = 6 units.

Which equation is true?

1)rY =1/2 rX
2)rY = 2πrX
3)rY = pi/3
4)rY = 3/pi

Answer 1

Correct choice is 4)

Explanation:

Circle X has radius
`r_X = 6` units and circumference
`C_X=12\pi` units.

Circle Y has radius
`r_Y` units and circumference
`C_Y = 6` units.

Then

`r_X\ -\ C_X,\\ \\r_Y\ -\ C_Y.`

Mathematically, you can write a proportion:

`(r_X)/(r_Y)=(C_X)/(C_Y),\\ \\(6)/(r_Y)=(12\pi)/(6),\\ \\r_Y=(6\cdot 6)/(12\pi)=(3)/(\pi)\ units.`

Answer 2

Writing the circumference of circle X and circle Y in ratio

`C_(Y): C_(X)`

`12 \pi :6 \pi`

`2:1`

Circumference of Y is twice of circumference of X, hence the radius of circle Y is twice of circle X

Correct answer: option 1)