In the figure below, two circles with centres $ A $ and $ B $ touch each other at the point $ C $. If $ A C=8 \mathrm{~cm} $ and $ A B=3 \mathrm{~cm} $, find the area of the shaded region. "

Given:

Two circles with centres \( A \) and \( B \) touch each other at the point \( C \).

\( A C=8 \mathrm{~cm} \) and \( A B=3 \mathrm{~cm} \).

To do:

We have to find the area of the shaded region.

Solution:

$BC = 8 - 3\ cm$

$= 5\ cm$

Radius of the bigger circle $R= 8\ cm$

Radius of the smaller circle $r = 5\ cm$

Therefore,

Area of the shaded region $=$ Area of the bigger circle $-$ Area of the smaller circle

$=\pi R^{2}-\pi r^{2}$

$=\frac{22}{7}(8^{2}-5^{2})$

$=\frac{22}{7}(64-25)$

$=\frac{22}{7} (39)$

$=122.57 \mathrm{~cm}^{2}$

The area of the shaded region is $122.57\ cm^2$.

Related Articles In the figure below, \( A B C D \) is a trapezium with \( A B \| D C, A B=18 \mathrm{~cm}, D C=32 \mathrm{~cm} \) and the distance between \( A B \) and \( D C \) is \( 14 \mathrm{~cm} \). Circles of equal radii \( 7 \mathrm{~cm} \) with centres \( A, B, C \) and \( D \) have been drawn. Then, find the area of the shaded region of the figure. (Use \( \pi=22 / 7) \)."\n
In the below figure, \( A B C D \) is a rectangle with \( A B=14 \mathrm{~cm} \) and \( B C=7 \mathrm{~cm} \). Taking \( D C, B C \) and \( A D \) as diameters, three semi-circles are drawn as shown in the figure. Find the area of the shaded region."\n
Find the area of the shaded region in the below figure, if \( A C=24 \mathrm{~cm}, B C=10 \mathrm{~cm} \) and \( O \) is the centre of the circle. (Use \( \pi=3.14) \)"\n
In the below figure, \( O A C B \) is a quadrant of a circle with centre \( O \) and radius \( 3.5 \mathrm{~cm} \). If \( O D=2 \mathrm{~cm} \), find the area of the shaded region."\n
In the below figure, \( A B C \) is a right angled triangle in which \( \angle A=90^{\circ}, A B=21 \mathrm{~cm} \) and \( A C=28 \mathrm{~cm} . \) Semi-circles are described on \( A B, B C \) and \( A C \) as diameters. Find the area of the shaded region."\n
In the figure below, \( A B C \) is an equilateral triangle of side \( 8 \mathrm{~cm} . A, B \) and \( C \) are the centres of circular arcs of radius \( 4 \mathrm{~cm} \). Find the area of the shaded region correct upto 2 decimal places. (Take \( \pi=3.142 \) and \( \sqrt{3}=1.732 \) )."\n
In the below figure, PSR, RTQ and \( P A Q \) are three semi-circles of diameters \( 10 \mathrm{~cm}, 3 \mathrm{~cm} \) and \( 7 \mathrm{~cm} \) respectively. Find the perimeter of the shaded region."\n
In the below figure, \( A B=36 \mathrm{~cm} \) and \( M \) is mid-point of \( A B . \) Semi-circles are drawn on \( A B, A M \) and \( M B \) as diameters. A circle with centre \( C \) touches all the three circles. Find the area of the shaded region."\n
In the figure, ABCD is a square of side 14 cm. With centres A, B, C and D, four circles are drawn such that each circle touch externally two of the remaining three circles. Find the area of the shaded region."
In the below figure, there are three semicircles, \( A, B \) and \( C \) having diameter \( 3 \mathrm{~cm} \) each, and another semicircle \( E \) having a circle \( D \) with diameter \( 4.5 \mathrm{~cm} \) are shown. Calculate the area of the shaded region."\n
In the below figure, \( A B C D \) is a trapezium of area \( 24.5 \mathrm{~cm}^{2} . \) In it, \( A D \| B C, \angle D A B=90^{\circ} \), \( A D=10 \mathrm{~cm} \) and \( B C=4 \mathrm{~cm} \). If \( A B E \) is a quadrant of a circle, find the area of the shaded region. (Take \( \pi=22 / 7) \)."\n
In the below figure, \( A B \) and \( C D \) are two diameters of a circle perpendicular to each other and OD is the diameter of the smaller circle. If \( O A=7 \mathrm{~cm} \), find the area of the shaded region."\n
In the below figure, \( A B C D \) is a rectangle, having \( A B=20 \mathrm{~cm} \) and \( B C=14 \mathrm{~cm} \). Two sectors of \( 180^{\circ} \) have been cut off. Calculate the area of the shadded region."\n
In the below figure, from a rectangular region \( A B C D \) with \( A B=20 \mathrm{~cm} \), a right triangle \( A E D \) with \( A E=9 \mathrm{~cm} \) and \( D E=12 \mathrm{~cm} \), is cut off. On the other end, taking \( B C \) as diameter, a semicircle is added on outside the region. Find the area of the shaded region. (Use \( \pi=22 / 7) \)."\n
In the below figure, a square \( O A B C \) is inscribed in a quadrant \( O P B Q \) of a circle. If \( O A=21 \mathrm{~cm} \), find the area of the shaded region."\n
Kickstart Your Career
Get certified by completing the course

Get Started