Three semicircles each of diameter 3 cm, a circle of diameter 4.5 cm and a semicircle of radius 4.5 cm are drawn in the given figure. Find the area of the shaded region. "
Given: Diameter of small semi-circles$=3\ cm$. Diameter of larger semi-circle$=4.5\ cm$ and radius of the circle$=4.5\ cm$.
To do: To find the area of the shaded region.
Solution:
Radius of small semi-circle$=\frac{Diameter}{2} =\frac{3}{2} \ cm$
radius of larger semi-circle$=4.5\ cm\ =\frac{9}{2}\ cm$
radius of the circle$=4.5cm\ =\frac{9}{2} \ cm$
Area of the shaded region $=$
[Area of the larger semi-circle]$-$[Area of the circle]$-2$[Area of the two small semi cirle$+$area of one small semi circle]
$=\frac{\pi }{2}\left(\frac{9}{2}\right)^{2} -\frac{\pi }{2}\left(\frac{9}{2}\right)^{2} -2\times$
Area of shaded region $=12.36\ cm$
Related Articles 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 figure, ABC is a quadrant of a circle of radius 14 cm and a semicircle is drawn with BC as diameter. Find the area of the shaded region."
In the given figure, ABCD is a rectangle of dimensions $21\ cm \times 14\ cm$. A semicircle is drawn with BC as diameter. Find the area and the perimeter of the shaded region in the figure. "\n
In figure, O is the centre of a circle such that diameter $AB=13\ cm$ and $AC=12\ cm$. $BC$ is joined. Find the area of the shaded region. $( Take\ \pi \ =\ 3.14)$"\n
Find the area of the shaded region in the given figure, if $ABCD$ is a square of side $14\ cm$ and $APD$ and $BPC$ are semicircles."
In Fig.5. PSR, RTQ and PAQ are three semicircles of diameters 10 cm, 3 cm and 7 cm respectively. Find the perimeter of the shaded region. [Use $\pi = 3.14$]"\n
In the figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If $OD = 2\ cm$, find the area of the shaded region."
Find the area of the shaded region in the given figure, if $PQ = 24\ cm, PR = 7\ cm$ and $O$ is the centre of the circle."
Find the diameter of the circle if radius is 6.2 cm.
Find the area of the shaded region if PAST is square of side 14 cm and ALS and PLT are semicircles."\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
Find the area of the shaded region, if $PQ=24 cm, PR=7 cm$, and O is the center of the circle."\n
In the figure, AB and CD are two diameters of a circle (with centre O) perpendicular to each other and OD is the diameter of the smaller circle. If $OA = 7\ cm$, find the area of the shaded region.
From each corner of a square of side 4 cm a quadrant of a circle of radius 1 cm is cut and also a circle of diameter 2 cm is cut as shown in the figure. Find the area of the remaining portion of the square."
In the figure, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If $OD = 2\ cm$, find the area of the (i) quadrant OACB.(ii) shaded region."
Kickstart Your Career
Get certified by completing the course
Get Started