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Question 46
In the following diagram there are four semi circular arcs and a shaded region. The diameter of largest semi circle is 28cm and of the smallest is 7cm. The area of shaded region is
Solution
we have :
28-7-7 =14
So we have 4 semicircles with diameters 28,7,7 and 14 .
Now area of shaded region = Area of bigger semicircle (radius 14 ) - 2 (Area of smaller semicircles with radius 3.5 ) +Area of semicircle with radius 7
we get $$\pi\ \ \frac{14^2}{2}-\ 2\ \frac{\pi\left(3.5\right)^2}{2}+\pi\ \ \frac{\left(7\right)^2}{2}$$
= $$98\pi+24.5\pi\ -12.25\pi\ \ =110.25\pi\ $$
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