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8. Curved Areas

The shape below is made up of quarter-circular arcs, each of radius r

Find its area in terms of r and pi
 

Scroll down the page for the answer.


 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

The shape is based around a square of side 4r as shown in the diagram

A = area of square - 4 semicircles + 4 threequartercircles
 
A = 16 r 2 - 2 pi r 2 + 3 pi r 2
 
A = 16 r 2 + pi r 2
 
A = (16 + pi) r 2
 

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