Math CentralQuandaries & Queries


Question from Geraldine, a student:

so ive been trying this question for an hour i know im getting close but i cant figure it out . here it goes

a wire bent into the shape of a square encloses an area of 25cm squared. then the same wire is cut and bent into two identical circles. what is the radius of one of the circles round to the nearest hundred

Hi Geraldine,

A square with area 25 cm squared = 52 cm squared has sides of length 5 cm. There are 4 sides so the wire is of length 4 × 5 = 20 cm.

If the wire is cut and then bent into two identical circles the wire must be cut in half. Thus half the wire length is the circumference of one of the circles. What is the formula for the circumference of a circle? In this formula you know the circumference and hence you can solve for the radius.

I hope this helps,

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