Class 10 Practice – Level 3 – Set 1 – Circles

Total questions: 15

The line segment joining the points of contact of two parallel tangent of a circle passes through its center. Is it true or not?

Topic: Tangents to a Circle

True

False

Cannot be determined

Incomplete information

None

The angle between the two tangents drawn from an external point to a circle is complementary to the angle subtended by the line-segment joining the points of contact at the center.

Topic: Angle Between Tangents

True

False

Incomplete information

Cannot be predicted

None

The parallelogram circumscribing a circle is:

Topic: Tangent to a Circle

Rhombus

Cyclic quadrilateral

Square

Kite

None

A horse is placed for grazing inside a rectangular field 70 m by 52 m. It is tethered to one corner by a rope 21 m long. Calculate the area which will be left ungrazed?

Topic: Area of a Sector of a Circle

4565.2 $ \displaystyle {{\text{m}}^{2}}$

3293.5 $ \displaystyle {{\text{m}}^{2}}$

2563.4 $ \displaystyle {{\text{m}}^{2}}$

4582.1 $ \displaystyle {{\text{m}}^{2}}$

None

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

Topic: Area of Path Around a Circle

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

$ \displaystyle 1256\text{ }{{\text{m}}^{2}}$

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

$ \displaystyle 1369\text{ }{{\text{m}}^{2}}$

None

The radius of a circle with centre O is 7 cm. Two radii OA and OB are drawn at right angles to each other. Find the areas of major segment.

Topic: Segments of a Circle

$ \displaystyle 153.06\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 127.75\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 253.01\text{ c}{{\text{m}}^{2}}$

$ \displaystyle 200.65\text{ c}{{\text{m}}^{2}}$

None

A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. Find the length of the arc and the area of the sector.

Topic: Area of a Sector of a Circle

36 cm, 577.5 sq. cm

44 cm, 477.8 sq. cm

55 cm, 577.5 sq. cm

29 cm, 677.1 sq. cm

None

What is the area of a ring whose outer and inner radii are respected 23 cm and 12 cm?

Topic: Area of a Ring

1452 $ \displaystyle c{{m}^{2}}$

1140 $ \displaystyle c{{m}^{2}}$

1358 $ \displaystyle c{{m}^{2}}$

1210 $ \displaystyle c{{m}^{2}}$

None

A wire when bent in the form of an equilateral triangle encloses an area of 121$ \displaystyle \sqrt{3}c{{m}^{2}}$. The same wire is bent to form a circle. What is the area enclosed by the circle.

Topic: Area of a Circle

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

$ \displaystyle 616c{{m}^{2}}$

$ \displaystyle 512c{{m}^{2}}$

$ \displaystyle 622c{{m}^{2}}$

None

10.

The length of an arc of a circle, subtending an angle of 54° at the center is 16.5 cm. What is the radius, circumference and area of the circle?

Topic: Arc Length and Circle Properties

18.5 cm, 145 cm, 756.5$ \displaystyle c{{m}^{2}}$

21.5 cm, 128 cm, 845.1$ \displaystyle c{{m}^{2}}$

17.5 cm, 110 cm, 962.5$ \displaystyle c{{m}^{2}}$

31.5 cm, 150cm, 985.2$ \displaystyle c{{m}^{2}}$

None

11.

If a square is inscribed in a circle, What is the ratio of the areas of the circle and the square.

Topic: Circle Inscribed with Square

π : 8

π : 3

π : 6

π : 2

None

12.

The side of a square is 10 cm. What should be (i) the area of the inscribed circle, and (ii) the area of the circumscribed circle? [take π =3.14 ]

Topic: Circle and Square

$ \displaystyle 78.57c{{m}^{2}}$, $ \displaystyle 157.14c{{m}^{2}}$

$ \displaystyle 98.77c{{m}^{2}}$, $ \displaystyle 136.12c{{m}^{2}}$

$ \displaystyle 50.21c{{m}^{2}}$, $ \displaystyle 234.10c{{m}^{2}}$

$ \displaystyle 88.75c{{m}^{2}}$, $ \displaystyle 418.57c{{m}^{2}}$

None

13.

The length of a chain used as the boundary of a semicircular park is 108 cm. What should be the area of park?

Topic: Semicircle and Area Calculation

875 $ \displaystyle {{m}^{2}}$

326 $ \displaystyle {{m}^{2}}$

693 $ \displaystyle {{m}^{2}}$

425 $ \displaystyle {{m}^{2}}$

None

14.

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

Topic: Quadrant of a Circle

$ \displaystyle \dfrac{{88}}{4}\text{c}{{\text{m}}^{2}}$

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

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

$ \displaystyle \dfrac{{32}}{6}\text{c}{{\text{m}}^{2}}$

None

15.

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

Topic: Circle Ratio of Circumference and Area

4 : 9

2 : 3

8 : 9

7 : 8

None

1 out of 15

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Class 10 Practice – Level 3 – Set 1 – Circles

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