Class 10 Practice – Level 2 – Set 2 – Circles

Total questions: 25

A path of 8 m width runs around the outsider of a circular park whose radius is 17 m. Find the area of the path.

Topic: Area of a Circular Path

$ \displaystyle 1189\text{ }{{\text{m}}^{2}}$

$ \displaystyle 1056\text{ }{{\text{m}}^{2}}$

$ \displaystyle 1044\text{ }{{\text{m}}^{2}}$

$ \displaystyle 1136\text{ }{{\text{m}}^{2}}$

None

The radius of the wheel of a vehicle is 42 cm. How many revolutions will it complete in a 19.8km long journey?

Topic: Revolutions of a Circular Wheel

5400

4500

2600

7500

None

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

Topic: Additional Grazing Area

$ \displaystyle638\text{ }{{\text{m}}^{2}}$

$ \displaystyle 587\text{ }{{\text{m}}^{2}}$

$ \displaystyle 858\text{ }{{\text{m}}^{2}}$

$ \displaystyle 769\text{ }{{\text{m}}^{2}}$

None

The area of a circle is 98.56 $ \displaystyle \text{c}{{\text{m}}^{2}}$. Find its circumference.

Topic: Circumference of a Circle

25.3 cm

54.2 cm

35.2 cm

66.4 cm

None

The circumference of a circle is 39.6 cm. What is the area?

Topic: Circumference of a Circle

124.74 sq.cm

145.36 sq.cm

136.25 sq.cm

134.25 sq.cm

None

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

Topic: Perimeter and Area

6 cm

8 cm

2 cm

4 cm

None

Find the area of the sector of a circle having radius 6 cm and angle 30°. (Take π = 3.14)

Topic: Area of a Sector of a Circle

$ \displaystyle 8.96\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 9.42\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 7.38\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 5.98\text{ c}{{\text{m}}^{2}}$

None

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

Topic: Area of a Sector of a Circle

$ \displaystyle 147\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 296\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 385\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 285\text{ c}{{\text{m}}^{2}}$

None

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

Topic: Radius of a Circle

12 cm

10 cm

16 cm

18 cm

None

10.

Find the perimeter of a semicircular protractor whose diameter is 14 cm.

Topic: Perimeter of a Semicircle

48 cm

56 cm

36 cm

24 cm

None

11.

The difference between the circumference and radius of a circle is 37 cm. Using π = $ \displaystyle \dfrac{{22}}{7}$, find the circumference of the circle.

Topic: Circumference of a Circle

36 cm

22 cm

57 cm

44 cm

None

12.

The circumference of a circle is 22 cm. What the area of its quadrant.

Topic: Area of a Quadrant

$ \displaystyle \dfrac{{66}}{4}\text{ c}{{\text{m}}^{2}}$

$ \displaystyle \dfrac{{77}}{8}\text{ c}{{\text{m}}^{2}}$

$ \displaystyle \dfrac{{85}}{5}\text{ c}{{\text{m}}^{2}}$

$ \displaystyle \dfrac{{32}}{8}\text{ c}{{\text{m}}^{2}}$

None

13.

A sheet of paper is in the from of rectangular ABCD in which AB = 40 cm and AD = 28 cm. A semi-circular portion with BC as diameter is cut off. Find the area of the remaining paper.

Topic: Area of Remaining Shape

$ \displaystyle 654\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 812\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 432\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 549\text{ c}{{\text{m}}^{2}}$

None

14.

What is the diameter of a circle whose area is equal to the sum of the areas of two circles of diameters 10 cm and 24 cm?

Topic: Diameter of a Circle

13 cm

36 cm

44 cm

26 cm

None

15.

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

Topic: Area of a Sector of a Circle

$ \displaystyle 1.02\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 3.05\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 5.12\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 2.10\text{ c}{{\text{m}}^{2}}$

None

16.

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

Topic: Radius of a Circle

35 cm

12 cm

64 cm

28 cm

None

17.

In the given figure, if O is the centre of a circle, PQ is a chord and the tangent PR at P makes an angle of 50° with PQ, then ∠POQ will be:

Topic: Angle Between Chord and Tangent

100°

80°

90°

75°

None

18.

In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 50°, then ∠OAB is equal to:

Topic: Angle Between Radius and Tangent

25°

30°

40°

50°

None

19.

If two tangents inclined at an angle 60° are drawn to a circle of radius 3 cm, then the length of each tangent is

Topic: Tangent to a Circle

$ \displaystyle \dfrac{3}{2}\sqrt{3}$ cm

6 cm

3 cm

$ \displaystyle 3\sqrt{3}$ cm

None

20.

If a, b, c are the sides of a right triangle where c is the hypotenuse. The radius r of the circle which touches the sides of the triangle is given by:

Topic: Incircle Radius of a Right Triangle

$ \displaystyle r=\dfrac{{a+b+c}}{2}$

$ \displaystyle r={{a+b+c}}$

$ \displaystyle r=\dfrac{{2a+2b+2c}}{2}$

$ \displaystyle r=\dfrac{{a+b+c}}{4}$

None

21.

If a circle touches the side BC of a triangle ABC at P and extended sides AB and AC at Q and R, respectively, Then AQ is equal to:

Topic: Tangents and Segments in a Triangle

$ \displaystyle \dfrac{1}{2}$ (BC + CA + AB)

$ \displaystyle \dfrac{1}{4}$ (BC + CA + AB)

$ \displaystyle \dfrac{1}{8}$ (BC + CA + AB)

$ \displaystyle \dfrac{2}{3}$ (BC + CA + AB)

None

22.

A circle touches all the four sides of a quadrilateral ABCD.Then the angles subtended at the centre of the circle by the opposite sides are ?

Topic: Tangents and Quadrilateral Properties

Equal

Complementary

Supplementary

None of these

None

23.

A quadrilateral ABCD is drawn to circumscribe a circle, then

Topic: Circumscribed Quadrilateral Properties

AB − CD = AD − BC

AB + CD = AD + BC

AB + AD = CD + BC

AC + BD = AD + BC

None

24.

From an external point P, tangents PA and PB are drawn to a circle with center O. If ∠PAB = 90°, then find ∠AOB.

Topic: Angle Between Tangents

120°

80°

100°

130°

None

25.

A circle inscribed in triangle ABC touches its sides AB, BC and AC at points D, E and F respectively. If AB = 12 cm, BC = 8 cm and AC = 10 cm, then find the lengths of AD.

Topic: Inradius and Lengths in a Triangle

4 cm

6 cm

7 cm

3 cm

None

1 out of 25

Time's up

Class 10 Practice – Level 2 – Set 2 – Circles

Welcome back