Area of a Segment

Q.

Two circles intersect as shown in the diagram below. The radii of the circles are $14cm$ each and $\angle AOP={45}^{\circ }$​ What is the area of the shaded region?

1. $132.5\pi sq.cm$

2. $156sq.cm$

3. $112sq.cm$

4. $56sq.cm$

Q.

Find the area of both the segments of a circle of radius 42 cm with central angle ${120}^{\circ }$. [ Given, sin ${120}^{\circ }=\frac{\sqrt{3}}{2}and\sqrt{3}$ = 1.73. ]

Q.

How would you find the area of the shaded region?

Consider the following steps. Which would be the correct order to solve the above-mentioned question?
1. Find the area of each unshaded region.
2. Identify the unshaded regions.
3. Subtract the sum total of areas of unshaded regions from the area of the square.

1. 2, 3, 1
2. 2, 1, 3
3. 3, 2, 1
4. 1, 2, 3

Q.

In the figure given below, the radius of the circle is 42cm. The angle in the sector is ${60}^{\circ }$​. What is the area of the segment APB?

1. $924sqcm$

2. $924-441\sqrt{3}sqcm$

3. $1743sqcm$

4. $441\sqrt{3}sqcm$

Q. Question 13
A round table cover has six equal designs as shown in Fig. 12.14. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of ₹ 0.35 per $c{m}^2.(Use\sqrt{3}=1.7)$

Q. Question 16
Calculate the area of the designed region in figure common between the two quadrants of circle of radius 8 cm each.

Q. In the given figure, two concentric circles with centre O have radii 21 cm and 42 cm. If $\angle$AOB = ${60}^{\circ }$, find the area of the shaded region. [Use $\pi =\frac{22}{7}$]

Q.

In the given fig. $\theta$ ABC is an equilateral triangle inscribed in a circle of radius 4 cm and centre O. Show that the area of the shaded region is $\frac{4}{3}(4\pi -3\sqrt{3})c{m}^2$. [4 MARKS]

Q. Question 202
Construct a trapezium RISK in which $RI\parallel KS$, RI = 7 cm, IS = 5 cm, RK = 6.5 cm and $\angle I={60}^{\circ }$.

Q.

In the given figure, a semicircle is drawn on the hypotenuse of the right-angled triangle. Another arc of radius 30 cm is drawn passing through A and C with O as the center. What is the area of the shaded region? (Take $\pi$ as 3.14 and $\sqrt{3}$ = 1.732)

1. $117.75sq.cm$

2. $271.95sq.cm$

3. $108sq.cm$

4. $216sq.cm$

Q. From each corner of a square of side $4cm$ a quadrant of a circle of radius $1cm$ is cut and also a circle of diameter $2cm$ is cut as shown in fig. Find the area of the remaining portion of the square.

Q. If the area of the circle is 100 sq.cm and the area of the major segment is 70 sq.cm, then the area of the minor segment of a circle is .

1. $170c{m}^2$
2. $30c{m}^2$
3. $130c{m}^2$

Q.

Figure shows a sector of a circle, centre O, containing an angle $\theta {}^{\circ }$. Prove that:

(i) Perimeter of the shaded region is $r(tan\theta +sec\theta +\frac{\pi \theta }{180}-1)$

(ii) Area of the shaded region is $\frac{r^2}{2}(tan\theta -\frac{\pi \theta }{180})$

Q.

Construct a cyclic quadrilateral PQRS with PQ = 6 cm, $\angle P={105}^{\circ }$ , $\angle PQS={45}^{\circ }$ and $\angle SQR={75}^{\circ }$.

Q. In the figure below, AB and CD are two diameters of a circle (with center 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.

1. 65.5 $c{m}^2$
2. 66.5 $c{m}^2$
3. 67.5 $c{m}^2$
4. 68.5 $c{m}^2$

Q. Calculate the area of the designed region in figure common between the two quadrants of circle of radius 8 cm each.

Q. In the following question, a statement of assertion (A) is followed by a statement of reason (R). ​

Mark the correct choice as:​

Assertion: In a circle of radius 6 cm, the angle of sector is $60°$. Then area of sector is $18\frac{6}{7}c{m}^2$.

Reason: The circumference of a circle with radius 𝒓 is 𝟐𝝅𝒓.

Q.

Question 12 (ii)
In Fig. 12.30, OACB is a quadrant of a circle with centre O and radius 3.5 cm. If OD = 2 cm, find the area of the:
(ii) shaded region.

Q.

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. [2 MARKS]

Q. In the given figure below, OACB is a quadrant of a circle. The radius OA = 3.5 cm, OD = 2 cm. Calculate the area of the shaded region.

1. 6.5 $c{m}^2$
2. 6.125 $c{m}^2$
3. 7 $c{m}^2$
4. 5.125 $c{m}^2$

Q.

In 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 $c{m}^2$).

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Q. If the area of the circle is 100 sq.cm and the area of the major segment is 70 sq.cm, then the area of the minor segment of a circle is .

1. $170c{m}^2$
2. $30c{m}^2$
3. $130c{m}^2$

Q. In the given figure, a triangle $ABC$ is drawn to circumscribe a circle of radius 3 cm such that the segments BD and DC into which BC is divided by the point of contact D, are of lengths 6 cm and 9 cm respectively. If the area of $\Delta ABC=54c{m}^2$ then find the lengths of sides AB and AC.

Q. Calculate the area of the designed region in figure common between the two quadrants of circle of radius 8 cm each.

Q. Match the following with the area of shaded regions in $c{m}^2$.

1. $\frac{250\pi }{3}$
2. $\frac{50\pi }{3}-25\sqrt{3}$
3. $\frac{50\pi }{3}$

Q. Match the following with the area of shaded regions in $c{m}^2$.

1. $\frac{250\pi }{3}$
2. $\frac{50\pi }{3}-25\sqrt{3}$
3. $\frac{50\pi }{3}$