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.
"
Given:
OACB is a quadrant of a circle with centre O and radius 3.5 cm.
$OD = 2\ cm$
To do:
We have to find the area of the
(i) quadrant OACB.
(ii) shaded region.
Solution:
(i) Radius of the quadrant $OACB = 3.5\ cm$
Area of the quadrant $\mathrm{OACB}=\frac{\pi r^{2} \theta}{360^{\circ}}$
$=\frac{22}{7} \times \frac{3.5 \times 3.5 \times 90^{\circ}}{360^{\circ}}$
$=\frac{22 \times 35 \times 35 \times 90^{\circ}}{7 \times 360^{\circ} \times 100}$
$=\frac{77}{8} \mathrm{~cm}^{2}$
The area of the quadrant OACB is $\frac{77}{8} \mathrm{~cm}^{2}$.
(ii) $OD = 2\ cm$
$OB = 3.5\ cm$
Therefore,
Area of the triangle $\mathrm{OBD}=\frac{1}{2} \times \mathrm{OB} \times \mathrm{OD}$
$=\frac{1}{2} \times 3.5 \times 2$
$=3.5 \mathrm{~cm}^{2}$
Area of the shaded region $=$ Area of the quadrant $-$ Area of the triangle $\mathrm{OBD}$
$=\frac{77}{8}-\frac{35}{10}$
$=\frac{77}{8}-\frac{7}{2}$
$=\frac{77-28}{8}$
$=\frac{49}{8} \mathrm{~cm}^{2}$
The area of the shaded region is $\frac{49}{8} \mathrm{~cm}^{2}$.
Related Articles 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."
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, \( O A C B \) 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 quadrant \( O A C B \)."\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."
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."
In the below figure, \( O A B C \) is a square of side \( 7 \mathrm{~cm} \). If \( O A P C \) is a quadrant of a circle with centre O, then 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
In the figure, a square $OABC$ is inscribed in a quadrant $OPBQ$. If $OA = 20\ cm$, find the area of the shaded region. (Use $\pi = 3.14$)"
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.
The circumference of a circle is $22\ cm$. Calculate the area of its quadrant $( in\ cm^{2})$.
Find the area of a quadrant of a circle whose circumference is 22 cm.
In the figure, $OCDE$ is a rectangle inscribed in a quadrant of a circle of radius $10\ cm$. If $OE = 2\sqrt5$, find the area of the rectangle."\n
In the below figure, a square \( O A B C \) is inscribed in a quadrant \( O P B Q \). If \( O A=15 \mathrm{~cm} \), find the area of shaded region (use \( \pi=3.14)."\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
Find the area of the shaded region, if $PQ=24 cm, PR=7 cm$, and O is the center of the circle."\n
Kickstart Your Career
Get certified by completing the course
Get Started