The minute hand of a clock is 15cm long. Find the area swept by it in 20minutes. Take π = 3.14

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જવાબ : Angle described by the minute hand in 60 minutes = 360°

A pendulum swings through an angle of 30 and describes an arc 8.8cm in length. What is the length of the pendulum?

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જવાબ : Length of pendulum = radius of sector = r cm

The circumference of a circle is 8 cm. What is the area of the sector whose central angle is 72°?

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જવાબ :

A square is inscribed in a circle. What is the ratio of the areas of the circle and the square?

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જવાબ :

The areas of two circles are in the ratio 4 : 9. Find the ratio between their circumferences.

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જવાબ :

The circumferences of two circles are in the ratio 2 : 3. Find the ratio between their areas.

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જવાબ :

In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre. What is the length of the arc?

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જવાબ :

What is the area of the sector of a circle having radius 6 cm and of angle 30°? [Take π = 3.14.]

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જવાબ :

What is the diameter of the circle whose area is equal to the sum of the areas of two circles having radii 4 cm and 3 cm?

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જવાબ :

What is the area of a circle whose circumference is 8π?

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જવાબ :

What is the perimeter of a semicircular protractor whose diameter is 14 cm?

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જવાબ :

The radii of two circles are 19 cm and 9 cm. What is the radius of the circle which has circumference equal to the sum of the circumferences of the two circles?

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જવાબ :

The radii of two circles are 8 cm and 6 cm. WJat is the radius of the circle having area equal to the sum of the areas of the two circles?

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જવાબ :

What is the radius of a circle whose perimeter and area are numerically equal?

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જવાબ :

Circumference of a circle is 39.6 cm. find its area.

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જવાબ : Circumference of circle = 2 *π*r = 39.6 cm

Circumference of a circle is 22 cm. Find the area of its quadrant.

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જવાબ :

A circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm, Find the Diameter

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જવાબ :

If the area of a circle is numerically equal to twice its circumference, then find the diameter of the circle.

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જવાબ :

Find the perimeter of a square which circumscribes a circle of radius a cm.

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જવાબ : Side of the square = 2 ⨯ radius of circle = 2a cm Then, Perimeter of the square = (4 ⨯ 2a) = 8a cm

What is the length of the arc of a circle of diameter 42 cm which subtends an angle of 60° at the centre?

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જવાબ :

A sector of 56^{o}, cut out from a circle, contains 17.6 cm^{2}. What is the radius of the circle

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જવાબ :

The area of the sector of a circle of radius 10.5cm is 69.3 cm^{2}. What is the central angle of the sector?

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જવાબ :

The perimeter of a certain sector of circle of radius 6.5cm is 31 cm. What is the area of the sector?

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જવાબ :

The radius of a circle is 17.5 cm. What is the area of the sector enclosed by two radii and an arc 44cm in length?

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જવાબ :

Two circular pieces of equal radii and maximum area, touching each other are cut out from a rectangular cardboard of dimensions 14 cm x 7 cm. What the area of the remaining cardboard?

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જવાબ :

ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. [Use π = 3.14.]

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જવાબ :

A rectangular sheet of paper ABCD with AB = 40 cm and AD = 28 cm, a semicircular portion with BC as diameter is cut off from that sheet. Find the area of the remaining paper.

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જવાબ :

OABC is a square of side 7 cm. If COPB is a quadrant of a circle with centre C find the area of the shaded region.

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જવાબ :

Three sectors of a circle of radius 7 cm, making angles of 60°, 80° and 40° at the centre are shaded. Find the area of the shaded region.

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જવાબ :

Find the area of the shaded region, if ABCD is a square of side 14 cm and APD and BPC are semicircles.

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જવાબ :

PQ and AB are respectively the arcs of two concentric circles of radii 7 cm and 3.5 cm with centre O. If ∠POQ = 30°, find the area of the shaded region.

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જવાબ :

ABCD is a square of side 7 cm, DPBA and DQBC are quadrants of circles each of the radius 7 cm. Find the area of shaded region.

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જવાબ :

AOBCA represents a quadrant of a circle of radius 3.5 cm with centre O. Calculate the area of the shaded portion.

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જવાબ :

Find the perimeter of the shaded region in the figure, if ABCD is a square of side 14 cm and APB and CPD are semicircles.

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જવાબ :

In a circle of radius 7 cm, a square ABCD is inscribed. Find the area of the circle which is outside the square.

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જવાબ :

The shape of the top of a table is that of a sector of a circle with centre 0 and ∠A0B =90°. If AO =0B = 42 cm, then find the perimeter of the top of the table.

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જવાબ :

APB and CQD are semicircles of diameter 7 cm each, while ARC and BSD are semicircles of diameter 14 cm each. Find the perimeter

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જવાબ :

PSR, RTQ and PAQ are three semicircles of diameter 10 cm, 3 cm and 7 cm respectively. Find the perimeter of shaded region. [Use π = 3.14.]

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જવાબ :

A square OABC is inscribed in a quadrant OPBQ of a circle. If OA = 20 cm, find the area of the shaded region. [Use π = 3.14.]

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જવાબ :

APB and AQO are semicircles and AO = OB. If the perimeter of the figure is 40 cm, find the area of the shaded region.

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જવાબ :

What is the area of a quadrant of a circle whose circumference is 44 cm?

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જવાબ :

Calculate area of the shaded region, where ABCD is a square of side 14cm and all circles are of the same diameter.

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જવાબ :

A square ABCD is inscribed in a circle of radius r. Calculate the area of the square.

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જવાબ :

A wire is bent to form a square enclosing an area of 484 m^{2}. Using the same wire, a circle is formed. Find the area of the circle.

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જવાબ :

Calculate the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

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જવાબ :

From a thin metallic piece in the shape of a trapezium ABCD in which AB ‖ CD and ∠BCD = 90°, a quarter circle BFEC is removed. Given, AB = BC = 3.5 cm and DE = 2 cm, Find the area of remaining (shaded) part of metal sheet.

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જવાબ :

O is the centre of the bigger circle, and AC is its diameter. Another circle with AB as diameter is draw. If AC = 54cm and BC = 10 cm, find the area of the shaded region.

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જવાબ :

PQSR represents a flower bed. If OP = 21 m and OR = 14 m, calculate the area of the flower bed.

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જવાબ : Area of flower bed = (area of quadrant OPQ)-(area of the quadrant ORS)

A park is in the form of a rectangle 120m by 90m. At the centre of the park there is a circular lawn as shown in the figure. The area of the park excluding the lawn is 2950 m^{2}. Calculate the radius of the circular lawn. (given: π =3.14)

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જવાબ :

The cost of fencing a circular field at the rate of Rs.25 per metre is Rs.5500. The field is to be ploughed at the rate of 50 paise per m^{2}. Calculate the cost of ploughing the field.

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જવાબ :

All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if the area of the circle is 1256 cm^{2}. [Use π = 3.14] (2015OD)

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જવાબ : In rhombus, AB = BC = CD = AD

⇒ AC = BD = 2r

In Figure, ABCD is a square of side 14 cm. Semi-circles are drawn with each side of square as diameter. Find the area of the shaded region. [Use π = 22/7] (2016D)

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જવાબ :

Area of shaded region = 2(Area of square) – 4(Area of semicircle) = 2 × 196 – 308 = 392 – 308 = 84 cmIn Figure, arcs are drawn by taking vertices A, B and C of an equilateral triangle ABC of side 14 cm as centres to intersect the sides BC, CA and AB at BZ their respective mid-points D, E and F. Find the area of the shaded region. [Use π = 22/7 and √3 = 1.73] (2011D)

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જવાબ : ∠ABC = ∠BAC = ∠ACB = 60°

Find the area of the shaded region in Figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-points P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD, where the length of each side of square is 14 cm. (Use π = 22/7) (2011D)

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જવાબ : Side = 14 cm, radius, r = 14/2 = 7 cm

Area of the shaded region = ar (square) – 4 (ar of quadrant)

In Figure, three circles each of radius 3.5 cm are drawn in such a way that each of them touches the other two. Find the area enclosed between these three circles (shaded region). [Use π = 22/7] (2011OD)

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જવાબ : AB = BC = CA

= 2(3.5) = 7 cm

=> ∆ABC is an equilateral ∆

Find the area of the shaded region in Figure, where ABCD is a square of side 28 cm. (2011OD)

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જવાબ : r = 28/4= 7 cm

Area of the shaded region = ar(square) – 4(circle) = (side)^{2} – 4 (πr^{2})

= (28)^{2} – 4 × 22/7 × 7 × 7 = 784 – 616 = 168 cm^{2}

In Figure, an equilateral triangle has been inscribed in a circle of radius 6 cm. Find the area of the shaded region. [Use π = 3.14] (2011OD)

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જવાબ : Here θ = 360/3] = 120°, r = 6 cm

Area of shaded region = 3(ar of minor segment) = 3[ar(minor sector) – ar(∆ABC)]

In Figure, PQRS is a square lawn with side PQ = 42 metres. Two circular flower beds are there on the sides PS and QR with centre at O, the inter- section of its diagonals. Find the total area of the two flower beds (shaded parts). (2015OD)

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જવાબ : PO = 42 m …[Given in the ques.

PS = QR …[∵ side of square

OR = OP …[Radius

Let OR be the radius of circle = x

So, PR = OR + OP = 2x

Using Pythagoras’ theorem,

⇒(PR)^{2} = (RQ)^{2} + (PQ)^{2}

⇒(2x)^{2} = (42)^{2} + (42)^{2}

In Figure, is shown a sector OAP of a circle with centre 0, containing ∠θ. AB is a perpendicular to the radius OA and meets OP produced at B. Prove that the perimeter of shaded region is r [tan θ + sec θ + πθ/180^{∘} – 1] (2016OD)

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જવાબ :

In the Figure, the side of square is 28 cm and radius of each circle is half of the length of the side of the square where 0 and Oare centres of the circles. Find the area of shaded region. (2017D)

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જવાબ : Side = 28 cm, Radius = 28/2 cm = 14 cm

The area of the shade = Area of square + 3/4 (Area of circle) + 3/4 (Area of circle)

= Area of square + 3/2 (Area of circle)

= (28)^{2} + 3/2 × 22/7× 14 × 14

= 784 + 924 = 1708 cm^{2}

A chord 10cm long is drawn in a circle whose radius is 5√2 cm. Find the areas of both the segments. Take π = 3.13

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જવાબ :

Find the areas of both the segments of a circle of radius 42 cm with central angle 120^{o}. ( sin120°= √3/2 and √3=1.73)

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જવાબ :

A chord of a circle of radius 30cm makes an angle of 60° at the centre of the circle. Find the areas of the minor and major segments. Take π = 3.14, √3 =1.732

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જવાબ :

In a circle of radius 10.5cm, the minor arc is one-fifth of the major arc. Find the area of the sector corresponding to the major arc.

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જવાબ :

The short and long hands of a clock are 4cm and 6cm long respectively. Find the sum of distances travelled by their tips in 2days. Take π = 3.14

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જવાબ :

Find the area of a quadrant of a circle whose circumference is 88 cm

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જવાબ :

A rope by which a cow is tethered is increased from 16m to 23m. How much additional ground does it have now to graze?

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જવાબ :

A horse is placed for grazing inside a rectangular field 70m by 52m. It is tethered to one corner by a rope 21 m long. On how much area can it graze? How much area is left ungrazed?

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જવાબ :

A horse is tethered to one corner of a field which is in the shape of an equilateral triangle of side 12m. If the length of the rope is 7m, find the area of the field which the horse cannot graze. Take √3 = 1.732 . Write the answer correct to 2 places of decimal.

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જવાબ :

Four cows are tethered at the four corners of a square field of side 50 m such that each can graze the maximum unshared area. What area will be left ungrazed? Take π = 3.14

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જવાબ :

Match the radius with the resp. area of sector of angle of 45°

1 |
2 |
A |
2π |

2 |
4 |
B |
9π/2 |

3 |
6 |
C |
π/2 |

4 |
8 |
D |
8π |

જવાબ :

1-C, 2-A, 3-B, 4-D

Match the radius with the resp. area of sector of angle of 90°

1 |
2 |
A |
9 π |

2 |
4 |
B |
π |

3 |
6 |
C |
16 π |

4 |
8 |
D |
4 π |

જવાબ :

1-B, 2-D, 3-A, 4-C

Match the radius with the resp. area of semi-circle

1 |
1/√π |
A |
8 |

2 |
2/√π |
B |
½ |

3 |
3/√π |
C |
2 |

4 |
4/√π |
D |
9/2 |

જવાબ :

1-B, 2-C, 3-D, 4-A

Match the radius with the resp. area of circle

1 |
1/√π |
A |
16 |

2 |
2/√π |
B |
9 |

3 |
3/√π |
C |
4 |

4 |
4/√π |
D |
1 |

જવાબ :

1-D, 2-C, 3-B, 4-A

Match the radius with the resp. area of semi-circle

1 |
8 |
A |
8 π |

2 |
6 |
B |
4 π |

3 |
4 |
C |
16π |

4 |
2 |
D |
32π |

જવાબ :

1-D, 2-C, 3-A, 4-B

જવાબ :

1-D, 2-C, 3-A, 4-B

Match the radius with the resp. perimeters of semi-circle

1 |
12 |
A |
12(π + 2) |

2 |
14 |
B |
16(π + 2) |

3 |
16 |
C |
14(π + 2) |

જવાબ :

1-A, 2-C, 3-B

Match the radius with the resp. perimeters of circle

1 |
12 |
A |
36π |

2 |
14 |
B |
24π |

3 |
16 |
C |
28π |

4 |
18 |
D |
32π |

જવાબ :

1-B, 2-C, 3-D, 4-A

Match the radius with the resp. perimeters of semi-circle

1 |
2 |
A |
6(π + 2) |

2 |
4 |
B |
2(π + 2) |

3 |
6 |
C |
8(π + 2) |

4 |
8 |
D |
4(π + 2) |

જવાબ :

1-B, 2-D, 3-A, 4-C

Match the radius with the resp. perimeters of circle

1 |
2 |
A |
8π |

2 |
4 |
B |
12π |

3 |
6 |
C |
4π |

4 |
8 |
D |
16π |

જવાબ :

1-C, 2-A, 3-B, 4-D

Math

Chapter 12 : Areas related to Circles

- Math Book for CBSE Class 10
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The GSEB Books for class 10 are designed as per the syllabus followed Gujarat Secondary and Higher Secondary Education Board provides key detailed, and a through solutions to all the questions relating to the GSEB textbooks.

The purpose is to provide help to the students with their homework, preparing for the examinations and personal learning. These books are very helpful for the preparation of examination.

For more details about the GSEB books for Class 10, you can access the PDF which is as in the above given links for the same.