Class 10 Practice – Level 2 – Set 2 – Areas Related to Circles

Total questions: 25

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the figure. Find:

Topic: Areas of Sectors a Circle

(i) The total length of the silver wire required.
(ii) The arc of each sector of the brooch

285 mm, 96.25 mm²

265 mm, 90.35 mm²

195 mm, 89.63 mm²

255 mm, 90.25 mm²

None

An umbrella has 8 ribs which are equally spaced. Assume umbrella to be a flat circle of radius 45 cm, then find the area between the two consecutive ribs of the umbrella.

Topic: Areas of Sectors a Circle

795.5 cm²

852.4 cm²

798.4 cm²

816.5 cm²

None

A car has two wipers which do not overlap. Each wiper has a blade of length 25 cm sweeping through an angle of 115°. Find the total area cleaned at each sweep of the blades.

Topic: Areas of Sectors a Circle

$\displaystyle \dfrac{158955}{365}$ cm²

$\displaystyle \dfrac{158976}{365}$ cm²

$\displaystyle \dfrac{158125}{126}$ cm²

$\displaystyle \dfrac{365998}{154}$ cm²

None

To warn ships for underwater rocks, a lighthouse spreads a red coloured light over a sector of angle 80° to a distance of 16.5 km. Find the area of the sea over which the ships are warned. (Use π=3.14)

Topic: Areas of Sectors a Circle

179.97 m²

199.97 km²

189.97 km²

185.97 km²

None

The area of a sector of angle p (in degrees) of a circle with radius R is:

Topic: Area of a sector formula

$\displaystyle \dfrac{P}{180}$ 2πR

$\displaystyle \dfrac{P}{360}$ πR²

$\displaystyle \dfrac{P}{720}$ 2πR²

$\displaystyle \dfrac{P}{720}$ πR²

None

If PQ=24cm,PR=7cm and O is the centre of the circle, then the area of the shaded region in the given figure will be:

Topic: Area of Segments in a Circle

141.54 cm²

161.54 cm²

151.54 cm²

151.26 cm²

None

Find the area of the shaded region in the given figure, if radii of the two concentric circles with center O are 7cm and 14cm respectively and ∠AOC=40°.

Topic: Area of Concentric Circles

51.33 cm²

45.33 cm²

62.53 cm²

51.99 cm²

None

In the given figure, OE=20 cm. In sector OSFT, square GOEF is inscribed. Find the area of the shaded region. [Use π=3.14].

Topic: Area of a sector with an inscribed square

228 cm²

265 cm²

365 cm²

245 cm²

None

Find the area of the shaded portion if each of the quadrants have radius as 7 cm. [Use π=$\displaystyle \dfrac{22}{7}$]

Topic: Properties of Area

42 cm²

65 cm²

45 cm²

32 cm²

None

10.

Find the area of the shaded design in the given figure, where ABCD is a square of side 10 cm and semicircles are drawn with each side of the square as diameter. (Use π=3.14)

Topic: Area of a square with semicircles

57 cm²

56 cm²

67 cm²

65 cm²

None

11.

In the given figure, O is the centre of a circle such that diameter AB=13 cm and AC=12 cm. BC is joined. Find the area of the shaded region. [Use π=3.14]

Topic: Area of Sector and Triangle in a Circle

56.33 cm²

46.33 cm²

36.33 cm²

49.33 cm²

None

12.

The area other than the area common between two quadrants of circles of radius 16 cm each which is shown as the shaded region in the given figure.

Topic: Area of Circular Segments and Intersection of Circles

109.20 cm²

206.20 cm²

230.20 cm²

109.72 cm²

None

13.

Four equal circles are described about the four corners of a square such that each touches two of the others as shown in the figure. Find the area of the region at the centre if each side of the square measures 14 cm.

Topic: Circle Inscribed in a Square

45 cm²

63 cm²

65 cm²

42 cm²

None

14.

The area of the square that can be inscribed in a circle of radius 8 cm is:

Topic: Area of an Inscribed Square in a Circle

158 cm²

78cm²

128 cm²

325 cm²

None

15.

The largest triangle is inscribed in a semi-circle of radius r, then the area of that triangle is:

Topic: Triangle Inscribed in a Semi-Circle

r²

2r²

4r²

None

16.

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is:

Topic: Circumference and Radius

28 cm

16 cm

18 cm

19 cm

None

17.

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m×16 m. Find the area of the field in which the cow can graze.

Topic: Properties of Area

154 cm²

254 cm²

325 cm²

124 cm²

None

18.

Find the area of the shaded field as shown in the figure.

Topic: Properties of Area

(65+ 2π)m²

(32 + 2π)m²

(45+ 2π)m²

(25+ 2π)m²

None

19.

Find the area of the shaded region in the given figure.

Topic: Properties of Area

(325−4π)m²

(265−4π)m²

(245−4π)m²

(248−4π)m²

None

20.

The radius of a circle whose circumference is equal to the sum of the circumferences of the two circles of diameters 36 cm and 20 cm is:

Topic: Circumferences of Circles

25 cm

28 cm

16 cm

26 cm

None

21.

The area of a sector of a circle of radius 28 cm and central angle 45° is:

Topic: Areas of Sectors a Circle

305 cm²

308 cm²

352 cm²

205 cm²

None

22.

A cow is tied with a rope of length 14 m at the corner of a rectangular field of dimensions 20 m×16 m. Find the area of the field in which the cow can graze.

Topic: Area of Segment and Sector

634 cm²

154 cm²

365 cm²

125 cm²

None

23.

In the given figure, AB is a diameter of the circle, AC=6 cm and BC=8 cm. Find the area of the shaded region. (Use π=3.14 )

Topic: Area of Segment and Sector

54.5 cm²

34.5 cm²

65.5 cm²

64.5 cm²

None

24.

Find the area of the shaded region in the given figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-point P, Q, R and S of the sides AB, BC, CD and DA respectively of a square ABCD. (use π=3.14 )

Topic: Area of Circular Segments and Intersecting Arcs

30.96 cm²

60.66 cm²

40.96 cm²

60.46 cm²

None

25.

A circular park is surrounded by a road 21 m wide. If the radius of the park is 105 m, then what is the area of the road?

Topic: Annular Region

63546 cm²

15246 cm²

12548 m²

12457 m²

None

1 out of 25

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Class 10 Practice – Level 2 – Set 2 – Areas Related to Circles

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