2169 /www/nrich/html/content/04/weekly/prob9/ 1 2010-08-07T13:24:30 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><br></br> <p>The large circles in each figure has the same radii. Which shaded area is the greatest?</p> <p style="text-align: center;"><mdo:image alt="" height="250" src="4-1.png" width="50"></mdo:image></p> <p style="text-align: center;"> </p> <p>If you liked this problem, <a href="http://nrich.maths.org/548">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0">Let the large circles have radius R. $$ Area A = 2 x \pi x ({1 \over 2}R)^2 = 1/2 \pi R^2 $$ $$ Area B = 3 x {1 \over 2} x R^2 x {\sqrt 3\over 2} = {3\over 4} \sqrt 3 R^2$$ $$ Area C = (2 R^2) - \pi R^2 = (4 - \pi)R^2 $$ $$ Area D = 2 x {1 \over 2} x R^2 = R^2 $$ $$ Area E = \pi R^2 (\sqrt 2 R)^2 = (\pi - 2)R^2 $$ <br></br></mdoxml> 2 3 0 0 0 1 0 Weekly Problem 39 - 2011 Secondary Mapping Document Area and volume US