Please help me with this math problem !?

Question

Thank you so much! =)

Please look at this picture that goes along with the problem:

http://i37.tinypic.com/n3k8zo.jpg

Heres the problem:

The figure shows a circle with radius r and center P and an arc length 6. The two radii shown are extended 3 units outside the circle. There is an arc of length x, which is part of a larger circle (not shown) also centered at P. What must x equal?

A.9

B.12

C.r+3

D. pi(r+3/3)

E.6r+18/r

can you please explain how you got the answer? i havent been in school for about 3 months so i totally forgot how to do this! i start school in a few days and i have to be able to explain how i answered.

thanks sooooo much.

Answer 1

dang! haha i took geometry last year and forgot everything too! but if i had to guess just from what i remember, id have to guess E. Best of Luck!

Answer 2

the pic was fine, no problems

the point here is that the arc of 6 and the arc of x subtend the same angle

that means the ratio of arc length to radius is the same

in other words:

6/r = x/(r+3)

or solving for x:

x=6(r+3)/r=(6r+18)/r

Answer 3

Hi, glad to help:

The important formula to use here is s = r * θ, where s is the arc length, r is radius, theta is angle.

Apply the formula to the inner piece:



                   6 = r * θ

                   θ = 6 / r

The angle for the small and big piece are the same, so use the formula again:

                x = (r+3)θ  = (r + 3)( 6 / r)       where I substituted θ = 6/r for the angle

                                                                and the radius is bigger this time

Multiply it out to get   x  =  (6r + 18) / r =      6 + 18/r     ***Answer  (E)****

Did you make a typo when you typed  in answer E? That should be the answer, except 6 shouldn't be multiplied with r.