The radius of the larger circle is twice as long as the radius of the smaller circle. The area of the donut is 75 pi . Find the radius of the smaller (inner) circle.?

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Answer 1 · 2017-07-20T16:38:09

The smaller radius is 5

Let r = the radius of the inner circle.

Then radius of the larger circle is #2r#

From the reference we obtain the equation for the area of an annulus :

#A = pi(R^2-r^2)#

Substitute 2r for R:

#A= pi( (2r)^2- r^2)#

Simplify:

#A= pi( (4r^2- r^2)#

#A= 3pir^2#

Substitute in the given area:

#75pi = 3pir^2#

Divide both sides by #3pi#:

#25 = r^2#

#r = 5#