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Mensuration — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSMensuration5 Marks
Question
In the given figure, a circle of diameter $21\ cm$ 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) $=21 \mathrm{~cm}$
$\therefore \text { Radius }(\mathrm{R})=\frac{21}{2} \mathrm{~cm}$
$\text { Area }=\pi \mathrm{R}^2=\frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}=\frac{693}{2} \mathrm{~cm}^2$
$=346.5 \mathrm{~cm}^2$
Diamerer of bigger circle $=\frac{2}{3}$ or $21$
$=14 \mathrm{~cm}$
$\therefore \text { Radius }\left(\mathrm{r}_1\right)=\frac{14}{2}=7 \mathrm{~cm}$
and area $=\pi \mathrm{r}_1^2=\frac{22}{7} \times 7 \times 7=154 \mathrm{~cm}^2$
Diameter of smaller circle $=\frac{1}{3}$ of $21$
$=7 \mathrm{~cm}$
$\therefore \text { Radius }\left(\mathrm{r}_2\right)=\frac{7}{2} \mathrm{~cm}$
$\text { and area }=\pi \mathrm{r}_2^2=\frac{22}{7} \times \frac{7}{2} \times \frac{7}{2}$
$=\frac{77}{2} \mathrm{~cm}=38.5 \mathrm{~cm}^2$
Area of shaded portion $=346.5-(154+38.5)=(346.5-192.5)=154 \mathrm{~cm}^2$

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