Areas Related to Circles

Which statement best summarizes the chapter "Areas Related to Circles"?

1. The chapter studies only the circumference of circles.
2. The chapter explains formulas for the area and circumference of circles, sectors, segments, semicircles, quadrants, annuli, and composite figures, enabling students to solve practical area-related problems.
3. The chapter studies only tangents.
4. The chapter has no practical applications.

Which concept is most frequently used in this chapter?

1. Similar triangles
2. Areas of sectors and segments
3. Probability
4. Statistics

Which formula gives the area of an annulus?

1. π(R+r)
2. π(R²-r²)
3. 2πR
4. πr²

The shaded region obtained by subtracting the area of a smaller circle from a larger circle is called:

1. Chord
2. Ring (Annulus)
3. Diameter
4. Radius

A quadrant subtends an angle of:

1. 45°
2. 90°
3. 180°
4. 360°

Which value of π is commonly used in Class 10 calculations?

1. 2.14
2. 3.14 or 22/7
3. 1.41
4. 4.14

If the radius of a circle is halved, the area becomes:

1. Half
2. One-fourth
3. Double
4. Four times

If the radius of a circle is doubled, its area becomes:

1. Double
2. Four times
3. Three times
4. Eight times

A sector with central angle 180 degrees is called a:

1. Quadrant
2. Semicircle
3. Minor Sector
4. Major Sector

The length of the arc of a sector with angle θ degrees is:

1. (θ/360) × 2πr
2. πr²
3. 2πr²
4. (1/2)πr²

The area of a sector of angle θ degrees is:

1. (θ/360)πr²
2. 2πr
3. πr²
4. (θ/180)πr

The area of a quadrant of radius r is:

1. πr²
2. (1/2)πr²
3. (1/4)πr²
4. 2πr

The area of a semicircle is:

1. πr²
2. (1/2)πr²
3. 2πr
4. (1/4)πr²

The circumference of a circle of radius r is:

1. πr²
2. 2πr
3. πd²
4. r²

What is the formula for the area of a circle of radius r?

1. 2πr
2. πr²
3. πd
4. r²

A solid cylinder is melted and recast into a sphere. If radius of cylinder is 3 cm and height 12 cm, find radius of sphere.

1. 3 cm
2. 4 cm
3. 5 cm
4. 6 cm

A hemisphere has radius 7 cm. Find its total surface area.

1. 308 cm²
2. 462 cm²
3. 616 cm²
4. 770 cm²

Find volume of a sphere of radius 6 cm. (π = 22/7)

1. 904.32 cm³
2. 904 cm³
3. 1000 cm³
4. 800 cm³

A cone has radius 3 cm and height 4 cm. Find its slant height.

1. 4 cm
2. 5 cm
3. 6 cm
4. 7 cm

A cylinder has radius 7 cm and height 10 cm. Find its curved surface area. (π = 22/7)

1. 440 cm²
2. 308 cm²
3. 220 cm²
4. 154 cm²

A semicircle has radius 14 cm. Find its perimeter.

1. 44 cm
2. 66 cm
3. 72 cm
4. 88 cm

Find ratio of areas of two circles with radii 3 cm and 6 cm.

1. 1:2
2. 1:3
3. 1:4
4. 2:3

A circle is inscribed in a square of side 14 cm. Find area of circle.

1. 154 cm²
2. 308 cm²
3. 616 cm²
4. 196 cm²

A sector has angle 90° and radius 14 cm. Find its area.

1. 154 cm²
2. 308 cm²
3. 77 cm²
4. 616 cm²

If area of circle is 154 cm², find radius (π = 22/7).

1. 5 cm
2. 7 cm
3. 8 cm
4. 6 cm

A wire is bent into a circle of radius 7 cm. Find its length.

1. 44 cm
2. 22 cm
3. 88 cm
4. 154 cm

Find the area of a ring formed by two circles of radii 14 cm and 7 cm.

1. 147π
2. 196π
3. 157π
4. 210π

A circular garden is divided into two equal semicircles. If radius is 10 m, find area of one semicircle.

1. 100π
2. 50π
3. 25π
4. 20π

A wheel has radius 21 cm. Find its circumference.

1. 132 cm
2. 144 cm
3. 126 cm
4. 154 cm

A circular park has radius 14 m. Find its area. (Take π = 22/7)

1. 616 m²
2. 484 m²
3. 308 m²
4. 440 m²

Rope length for cow to graze 616 sq meters

1. 12
2. 14
3. 16
4. 18

Length of arc APB (formula from figure set)

1. option a
2. 2π
3. 3π
4. 4π

Radius 4cm, angle 60°. Area of segment OAPB (repeat)

1. option a
2. (8π/3–4√3)
3. option c
4. 4π

Length of arc APB (general formula)

1. θ/360×2πr
2. option b
3. option c
4. option d

Area of sector OAPB (repeat for set of questions)

1. πr²θ/360
2. option b
3. option c
4. option d

Quadrant of circle with circumference 44cm. Area of quadrant is

1. 154cm²
2. 38.5cm²
3. 77cm²
4. 22cm²

Sector radius 5cm, angle 72°. Area is

1. 25π
2. 20π
3. 15π
4. 5π

Shaded area between concentric circles radii 7cm and 14cm (sector with angle=90°) is

1. 42π
2. 84π
3. 21π
4. 27π

Length of arc APB, angle 30°, radius 6cm is

1. π
2. 2π
3. 3π
4. 4π

Radius 4cm, angle 60°. Area of segment OAPB is

1. (8π/3–4√3)
2. (8π/3–4√3)
3. (4π/3–√3)
4. 4π

Area of sector OAPB (formula question)

1. πr²θ/360
2. θ/360×πr
3. πr²θ/180
4. 2πrθ/360

Wheel radius 40cm. Revolutions in 20 seconds at speed 22m/s is

1. 500
2. 150
3. 175
4. 250

Two circles radii 3cm and 4cm. Radius of circle with area equal to sum of their areas is

1. 5cm
2. 7cm
3. 8cm
4. 9cm

Two car wipers, each blade 25cm, angle 115°. Total area cleaned is

1. 478.29cm²
2. 627.48cm²
3. 444cm²
4. 528cm²

Fencing circular field at Rs12/m costs Rs2640. Area of circle is

1. 3300m²
2. 3850m²
3. 4400m²
4. 5500m²

Round table cover radius 28cm, 6 equal designs (segments of 60° each). Cost at Rs.3.50/cm² is

1. Rs 1902
2. Rs 2170
3. Rs 1000
4. Rs 1626.80

If diameter of circle is d, area is

1. πd²
2. π(d/2)²
3. πd²/4
4. πd

Minute hand 28cm. Area swept in 15 minutes is

1. 308cm²
2. 784cm²
3. 896cm²
4. 616cm²

Area between concentric circles radii 21cm and 7cm is

1. 1156cm²
2. 1232cm²
3. 1330cm²
4. 1460cm²

Square ABCD side 14cm, two semicircles. Shaded area is

1. 21cm²
2. 42cm²
3. 63cm²
4. 84cm²

Square ABCD each side 28cm, four circles inscribed. Shaded area is

1. 42cm²
2. 84cm²
3. 168cm²
4. 336cm²

Square ABCD side 2cm. Area of shaded region (four quarter circles at corners) is

1. 2–π
2. 7–π
3. 4–π
4. 8–π

Horse tied by 10m rope at center of field. Area grazed is

1. 50π cm²
2. 75π cm²
3. 100π cm²
4. 150π cm²

Circle inscribed in square of side 10cm. Shaded area (circle minus overlap region) is

1. 57cm²
2. 114cm²
3. 171cm²
4. 228cm²

Umbrella 8 ribs, radius 42cm. Area between two consecutive ribs is

1. 660cm²
2. 693cm²
3. 770cm²
4. 774cm²

Chord of circle radius 6cm, angle 60°. Area of corresponding segment is

1. 3.27cm²
2. 6cm²
3. 6.8cm²
4. 3cm²

Radius 42cm, arc subtends 60°. Length of arc is

1. 22cm
2. 44cm
3. 66cm
4. 88cm

Area of sector is 1/6 of area of circle. Angle made by sector is

1. 80°
2. 70°
3. 60°
4. 90°

Chord of radius 15cm, angle 60°. Major and minor segment areas [π=3.14,√3=1.73]

1. 681cm², 25cm²
2. 706cm², 26.43cm²
3. 680.07cm², 26.43cm²
4. 686.07cm², 20.43cm²

Circle radius 21cm, arc 60°. Minor and major segment areas are

1. 41cm², 1355cm²
2. 40cm², 1255cm²
3. 40.05cm², 1155cm²
4. 39.05cm², 1100cm²

Circle radius 21cm, arc subtends 60°. Arc length and sector area are

1. 22cm, 231cm²
2. 11cm, 200cm²
3. 44cm, 100cm²
4. 11cm, 241cm²

Radius 14cm, sector area 102.7cm². Central angle is

1. 30°
2. 45°
3. 60°
4. 90°

Two concentric sector areas with r=7m and r=3.5m, angle=30°. Shaded area is

1. 9.625cm²
2. 9cm²
3. 10cm²
4. 8.5cm²

Sector from circle radius 42cm, angle 120°. Arc length and area are

1. 44cm, 924cm²
2. 88cm, 1848cm²
3. 132cm, 824cm²
4. 42cm, 1048cm²

Sector of circle, radius 6cm, angle 60°. Area and perimeter are

1. 18.86cm², 18.28cm
2. 18.76cm², 18.14cm
3. 18cm², 28cm
4. 17cm², 17.14cm

Circular pond diameter 17.5m, surrounded by path 3.5m wide. Area of path is

1. 231m²
2. 261m²
3. 241m²
4. 281m²

Square of side 4cm inscribed in circle. Area between circle and square is

1. (8π–16)cm²
2. (8π–16)cm²
3. (16π–16)cm²
4. 16cm²

Two circles touch externally, sum of areas=130π cm², distance between centers=14cm. Radii are

1. 14cm, 3cm
2. 11cm, 3cm
3. 7cm, 3cm
4. 28cm, 6cm

Square wire of area 121cm² bent into circle. Area of circle is

1. 22 cm²
2. 154 cm²
3. 44 cm²
4. 77 cm²

Wire bent into square has area 196cm². When bent into circle, area of circle is

1. 233 cm²
2. 626 cm²
3. 154 cm²
4. 245 cm²