Question

Match the following figures with their areas.

• A. $A-\left(i\right),B-\left(iii\right),C-\left(ii\right)$
• B. $A-\left(i\right),B-\left(ii\right),C-\left(iii\right)$
• C. $A-\left(iii\right),B-\left(ii\right),C-\left(i\right)$
• D. $A-\left(iii\right),B-\left(i\right),C-\left(ii\right)$

Answer 1

The correct option is D

$A-\left(iii\right),B-\left(i\right),C-\left(ii\right)$

A) Radius of bigger semi-circle $=14cm$
Area of bigger semi-circle
$=\frac{1}{2}\pi r^2=\frac{1}{2}\times \frac{22}{7}\times 14\times 14=308c{m}^2$

Now, radius of each of the smaller circle $=7cm$
Area of two smaller semi-circles
$=2(\frac{1}{2}\times \frac{22}{7}\times 7^2)=154c{m}^2$
$\therefore$ Required area $=308+154=462c{m}^2$

B) Radius of the smaller circle $=21cm$
Radius of the bigger circle $=21+3.5=24.5cm$
$\therefore$ Area of the path $=\left[\pi \right(24.5{)}^2-\pi \left(21{)}^2\right]=\left[\pi \right(24.5{)}^2-\left(21{)}^2\right]=\pi (24.5+21)(24.5-21)=\pi \left[\right(45.5)\times (3.5\left)\right]$
$\therefore$ Area of the path $=\frac{22}{7}\times 45.5\times 3.5=500.5c{m}^2$

C) Required area
$=$ Area of sector of angle ${30}^{\circ }$ with radius $7cm-$ Area of sector of angle ${30}^{\circ }$ with radius $3.5cm$
$=(\frac{{30}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times 7^2)-(\frac{{30}^{\circ }}{{360}^{\circ }}\times \frac{22}{7}\times {3.5}^2)=(\frac{77}{6}-\frac{77}{24})=\frac{77}{24}\times 3=\frac{77}{8}=9.625c{m}^2$