# Area of a Segment of a Circle

## Trending Questions

**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 π = 3.14]

**Q.**

A chord PQ of a circle of radius 10 cm subtends an angle of 60∘ 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 14 cm 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 cm, then the area of the shaded region is

- 25 sq. cm
- 2514 sq. cm
- 252 sq. cm
- 2516 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√2 cm. Find the areas of both the segments.

[Takeπ=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∘ at the centre of the circle. Find the area of the minor segment of the circle. (Use π=227)

**Q.**

AB is the diameter of a circle, centre O. C is a point on the circumference such that ∠COB=θ. The area of the minor segment cut off by AC is equal to twice the area of the sector BOC. Prove that sinθ2 cosθ2=π(12−θ120).

**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 cm^{2}. [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 ∠AOC=40∘.

**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 π=3.14)

**Q.**

Find the area of the major segment APB of a circle of radius 35 cm and ∠AOB = 90 ∘, 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∘ at the centre. Find the area of the corresponding major segment of the circle. (Use π=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∘ at the centre. If √3 = 1.73 then the area of the segment of the circle is

(a) 120.56cm2 (b) 124.63cm2 (c) 118.24cm2 (d) 130.57cm2

**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 √3=1.73andπ=227.]

**Q.**

A chord PQ of length 12 cm subtends an angle of 120∘ 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 θ 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 8 sin θ2 cos θ2+π=πθ45

**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.

- 6.5 cm2
- 6.125 cm2
- 7 cm2
- 5.125 cm2

**Q.**

^{2}. Find the area of its corresponding major sector. ( $\mathrm{\pi}$ = 3.14 )

**Q.**

Find the area of the minor segment of a circle of radius 14 cm, when the angle of the corresponding sector is 60∘.

**Q.**In the given figure, ΔABC is a right-angled triangle in which ∠A is 90∘. 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 100 cm2 and the area of the major segment is 70 cm2.

- 170 cm2
130 cm2

- 30 cm2
- 200 cm2

**Q.**

A circle having radius 4cm contains a chord of length 4cm and subtends an angle of 60 degrees. Find the area (in cm2)of the minor segment of the chord.

2

1.5

3

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 :

52 cm

^{2}60 cm

^{2}30 cm

^{2}40 cm

^{2}

**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)

37 cm

38 cm

37.68 cm

19 cm

37.5 cm