2166
/www/nrich/html/content/04/weekly/prob6/
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2010-09-29T09:40:38
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<p>The diagram shows a semi-circle containing a circle which touches the circumference of the semicircle and goes through its centre. What fraction of the semicircle is shaded?</p>
<p style="text-align: center;"><mdo:image alt="Semi Circle containing a circle" height="90" src="1-1.png" width="175"></mdo:image></p>
<p> </p>
<p>If you liked this problem, <a href="http://nrich.maths.org/public/viewer.php?obj_id=2161&refpage=titlesearch.php">here is an NRICH task</a> which challenges you to use similar mathematical ideas.</p></mdoxml>
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<p>Ans: ½</p>
<p>Let the radius of the circle be r. This implies that the radius
of the semicircle is 2r. The area of the semi circle is $1/2 \times
\pi \times(2r)^2$, which is twice the area of the small circle.</p>
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Weekly Problem 36 - 2011
Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?
Secondary Mapping Document
Area and volume LS