Math CentralQuandaries & Queries


Question from michael, a student:

a circle is drawn in a square PQRS. If the total area of the shaded portion of the square is 42 cm square, calculate the radius of the circle

Hi Michael,

Suppose the radius of the circle is $r$ cm then in the diagram you sent the square has side length $2 \times r$ cm.

circle in a square

The shaded region is the square with the circle removed and hence the area of the shaded region is the area of the square minus the area of the circle. The area of the square is $(2 \times r)^2$ square centimeters and the area of the circle is $\pi \; r^2$ square centimeters. Thus

\[(2 \times r)^2 - \pi \; r^2 = 42 \mbox{ square centimeters.}\]

Solve for $r.$


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