Area of a Segment of a Circle

Q.

A chord of a circle of radius 10 cm subtends a right angle at the centre. Find the area of the minor segment.

[ Use $\pi$ = 3.14]

Q.

A chord PQ of a circle of radius 10 cm subtends an angle of ${60}^{\circ }$ at the centre of the circle. Find the area of major and minor segments of the circle.

Q.

A chord of a circle of radius $14cm$ makes a right angle at the center. Find the areas of the minor and major segments of the circle.

Q. In the given figure, if the length of the diagonal of a square which is inscribed in the circle is $5\text{cm}$, then the area of the shaded region is

1. $25\text{sq. cm}$
2. $\frac{25}{14}\text{sq. cm}$
3. $\frac{25}{2}\text{sq. cm}$
4. $\frac{25}{16}\text{sq. cm}$

Q.

About $650,000$ people live in a circular region with a $6$-mile radius.

Find the population density in people per square mile.

Q.

A chord 10 cm long is drawn in a circle whose radius is $5\sqrt{2}$ cm. Find the areas of both the segments.

$[Take\pi =\mathrm{3.14.}]$

Q.

A chord of a circle of radius 15 cm subtends an angle of 60° at the centre. Find the areas of the corresponding minor and major segments of the circle.

[Use π = 3.14 and]

Q.

A chord AB of a circle, of radius 14 cm makes an angle of ${60}^{\circ }$ at the centre of the circle. Find the area of the minor segment of the circle. (Use $\pi =\frac{22}{7}$)

Q.

AB is the diameter of a circle, centre O. C is a point on the circumference such that $\angle COB=\theta$. The area of the minor segment cut off by AC is equal to twice the area of the sector BOC. Prove that $sin\frac{\theta }{2}cos\frac{\theta }{2}=\pi (\frac{1}{2}-\frac{\theta }{120})$.

Q.

A round table cover has six equal designs as shown in figure. If the radius of the cover is 28 cm, find the cost of making the designs at the rate of Rs.0.35 per cm². [Use]

Q. Question 2
Find the area of the shaded region in Fig. 12.20, if radii of the two concentric circles with centre O are 7 cm and 14 cm respectively and $\angle AOC={40}^{\circ }$.

Q.

In Fig. an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take $\pi =3.14$)

Q.

Find the area of the major segment APB of a circle of radius 35 cm and $\angle$AOB = 90 ${}^{\circ }$, as shown in the given figure.

Q. AB is a chord of a circle with centre O and radius 4 cm. AB is of length 4 cm and divides the circle into two segments. Find the area of the minor segment.

Q.

A chord of a circle of radius 20 cm subtends an angle of ${90}^{\circ }$ at the centre. Find the area of the corresponding major segment of the circle. (Use $\pi =3.14$)

Q.

Oil spilled from a ruptured tanker spreads in a circle whose area increases at a constant rate of $6{\mathrm{m}\mathrm{i}}^2/\mathrm{h}$.

How fast is the radius of the spill increasing when the area is $9{\mathrm{m}\mathrm{i}}^2?$

Q.

In a circle of radius 14 cm, an arc subtends an angle of ${120}^{\circ }$ at the centre. If $\sqrt{3}$ = 1.73 then the area of the segment of the circle is

(a) $120.56c{m}^2$ (b) $124.63c{m}^2$ (c) $118.24c{m}^2$ (d) $130.57c{m}^2$

Q.

On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. Find the covered area of the design.

[Use $\sqrt{3}=1.73and\pi =\frac{22}{7}$.]

Q.

A chord PQ of length 12 cm subtends an angle of ${120}^{\circ }$ at the centre of a circle. Find the area of the minor segment cut off by the chord PQ.

Q.

A chord of a circle subtends an angle of $\theta$ at the centre of the circle. The area of the minor segment cut off by the chord is one eighth of the area of the circle. Prove that $8sin\frac{\theta }{2}cos\frac{\theta }{2}+\pi =\frac{\pi \theta }{45}$

Q. Question 4
Is it true to say that area of segment of a circle is less than the areas of its corresponding sector? Why?

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.

Q.

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is ${60}^{\circ }$.

Q. In the given figure, $\Delta ABC$ is a right-angled triangle in which $\angle A$ is ${90}^{\circ }.$ Semicircles are drawn on AB, AC and BC as diameters. Find the area of the shaded region.

Q.

Find the area of the minor segment of a circle if the area of the circle is $100c{m}^2$ and the area of the major segment is $70c{m}^2$.

1. $170c{m}^2$

2. $130c{m}^2$

3. $30c{m}^2$
4. $200c{m}^2$

Q.

A circle having radius 4cm contains a chord of length 4cm and subtends an angle of 60 degrees. Find the area (in $c{m}^2$)of the minor segment of the chord.

1. 2

2. 1.5

3. 3

4. None of these

Q.

The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of minor and major segments.

Q.

AB is the diameter of a circle of radius 6.5 cm. If the length of chord CA is 5 cm then, the area of ΔABC IS :

1. 52 cm²

2. 60 cm²

3. 30 cm²

4. 40 cm²

Q.

PS is the diameter of a circle of radius 6 cm. Q and R are points on the diameter such that PQ, QR and RS are equal. Semicircles are drawn with PQ and QS as diameters, as shown in the figure. Find the perimeter of the shaded region.(take π = 3.14)

1. 37 cm

2. 38 cm

3. 37.68 cm

4. 19 cm

5. 37.5 cm