Class 10 Quiz Level 3 (Difficult) – Area Related to Circles

Total questions: 10

On a square cardboard sheet of area 784 cm², four congruent circular plates of maximum size are placed such that each circular plate touches the other two plates and each side of the square sheet is tangent to two circular plates. Find the area of the square sheet not covered by the circular plates.

Topic: Area of an Inscribed Square in a Circle

Deselect Answer

168 cm²

154 cm²

356 cm²

164 cm²

None

AB and CD are arcs of two concentric circles of radii 21 cm and 7 cm and centre 'O'. If ∠AOB=30°, then find the area of the shaded region.

Topic: Area of Concentric Circles

Deselect Answer

122.667 cm²

102.667 cm²

112.567 cm²

132.467 cm²

None

The wheels of a car are of diameter 80 cm each. How many complete revolutions does each wheel make in 10 minutes when the car is travelling at a speed of 66 km per hour?

Topic: Revolutions of a Wheel

Deselect Answer

4375

4338

5020

5523

None

In the given figure, ABCD is a trapezium with AB∥DC, AB=18 cm, DC=32 cm and distance between AB and DC=14 cm. If arcs of equal radii 7 cm with centres A, B, C, and D have been drawn, then, find the area of the shaded region of the figure.

Topic: Areas of Circular Segments

Deselect Answer

196 cm²

156 cm²

146 cm²

365 cm²

None

In the given figure, arcs are drawn by taking vertices A, B, and C of an equilateral triangle of side 10 cm to intersect the sides BC, CA, and AB at their respective mid-points D, E, and F. Find the area of the shaded region. (Use π=3.14)

Topic: Area of Arcs in an Equilateral Triangle

Deselect Answer

65.85 cm²

56.26 cm²

39.25 cm²

56.25 cm²

None

A calf is tied with a rope of length 6 m at the corner of a square grassy lawn of side 20 m. If the length of the rope is increased by 5.5 m, find the increase in area of the grassy lawn in which the calf can graze.

Topic: Areas of Circular Segments

Deselect Answer

75.625 m²

45.625 m²

25.625 m²

36.625 m²

None

All the vertices of a rhombus lie on a circle. Find the area of the rhombus, if area of the circle is 1256 cm². (Use π=3.14 )

Topic: Area of a Rhombus Inscribed in a Circle

Deselect Answer

800 cm²

400 cm²

500 cm²

600 cm²

None

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: Properties of Area

Deselect Answer

16.87 cm²

28.56 cm²

36.33 cm²

36.92 cm²

None

The cost of fencing a circular field at the rate of ₹24 per metre is ₹5280. The field is to be ploughed at the rate of ₹ 0.50 per m². Find the cost of ploughing the field (Take π= $\displaystyle \dfrac{22}{7}$ ).

Topic: Areas of Circular Segments

Deselect Answer

₹1565

₹1925

₹2232

₹2000

None

10.

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

Deselect Answer

$\displaystyle \dfrac{145}{3}$ cm²

$\displaystyle \dfrac{154}{3}$ cm²

$\displaystyle \dfrac{365}{6}$ cm²

$\displaystyle \dfrac{194}{5}$ cm²

None

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Class 10 Quiz Level 3 (Difficult) – Area Related to Circles

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