Math CentralQuandaries & Queries


Question from Bethany, a student:

The perimeter of a quarter circle is 3.57. What is the quarter circle's radius?

Hi Bethany,

The perimeter of a quarter circle is composed of three pieces, two are straight and are radii of the circle and the third piece is curved and is one-quarter of the circumference (perimeter) of the circle.

quarter circle

Suppose the radius of the circle is $r$ units. The perimeter of the quarter circle is then $r + r + \mbox{ one-quarter the circumference of the circle.}$ What is the expression for the circumference of a circle of radius $r$ units. Solve for $r.$


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