Word Problem

[troublemaker676]

Not sure if I got this question right:

If an arc of 45 degrees on circle A has the same length as an arc of 30 degrees on circle B, then the ratio of circle A to the area of circle B is

A 4/9 B 2/3 C 5/6 D 3/2 E 9/4

I got D 3/2, i did 45 divided by 30 which got me 1.5=3/2.

Is this right?

 

[stapel]

On what logical basis did you divide the angle measures?

Since it takes 45° of arc on A to get the same length as 30° of arc on B, then B must be the bigger circle, so getting a ratio that says A is bigger is unlikely to indicate a valid process.

Let the radius of A be "r" and the radius of B be "R". Use these variables to form expressions for the indicated arc lengths. Set the expressions equal. Solve for "R=", so you have B's radius in terms of A's.

Create the two area formulas. For "R" in B's area, plug in the expression you derived (above). For the ratio of the two expressions, and simplify.

Eliz.