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Mensuration — Maths STD 7 — Question

Maharashtra BoardEnglish MediumSTD 7MathsMensuration4 Marks
Question
In the given figure, a circle of diameter 21cm is given. Inside this circle, two circles with diameters $\frac{2}{3}$ and $\frac{1}{3}$ of the diameter of the big circle have been drawn, as shown in the given figure. Find the area of the shaded region.
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Answer

Diameter of largest circle (outer circle) }=$21 cm$
$\therefore \text { Radius }(R)=\frac{21}{2} cm$
$\text { Area }=\pi R^2=\frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}=\frac{693}{2} cm^2$
$=346.5 cm^2$
Diamerer of bigger circle $=\frac{2}{3}$ or 21
$=14 cm$
$\therefore \operatorname{Radius}\left(r_1\right)=\frac{14}{2}=7 cm$
and area $=\pi r_1^2=\frac{22}{7} \times 7 \times 7=154 cm^2$
Diameter of smaller circle $=\frac{1}{3}$ of 21
$=7 cm$
$\therefore \text { Radius }\left(r_2\right)=\frac{7}{2} cm$
and area $=\pi r_2^2=\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}$
$=\frac{77}{2} cm=38.5 cm^2$
Area of shaded portion $=346.5-(154+38.5)=(346.5-192.5)=154 cm^2$

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