Class 10 Practice – Level 1 – Areas Related to Circles Leave a Comment / By Gulam Hamza / September 19, 2024 Class 10 Practice – Level 1 – Areas Related to Circles Total questions: 40 1. What is the diameter of a circle whose area is equal to the sum of the area of two circles of diameters 10 cm and 24 cm? Topic: Area of a Circle Using Diameters 26 cm 35 cm 52 cm 56 cm None 2. The short and long hands of a clock are 4 cm and 6 cm long respectively. Find the sum of distance travelled by their tips in 2 days. Topic: Distance Travelled by Clock Hands 1519.3 cm 1910.8 cm 1010.8 cm 1510.6 cm None 3. The area of the major segment APB of a circle of radius 35 cm and ∠AOB= 90°, as shown in the given figure is: Topic: Area of Major Segment 8500 cm² 5500 cm² 3500 cm² 6500 cm² None 4. The circumference and area of the circle of radius 17.5 cm will be: Topic: Circumference and Area of a Circle 952.8 cm² ,810 cm 962.5 cm² ,110 cm 960.5 cm² ,120 cm 860.5 cm² ,110 cm None 5. If the circumference of a circle is 22 cm, then (i) its area and (ii) area of its quadrant will be: Topic: Area and Quadrant of a Circle 38.5 cm² ,9.625 cm² 88.5 cm² ,6.625 cm² 36.5 cm² ,4.625 cm² 46.5 cm² ,4.625 cm² None 6. The areas of two circles are in the ratio 9:4, then what is the ratio of their circumferences? Topic: Ratio of Areas and Circumferences 3 : 2 8 : 4 5 : 2 4: 1 None 7. The circumference of a circle is 39.6 cm. Find its area. Topic: Area from Circumference 124.74 cm² 454.74 cm² 564.85 cm² 204.85 cm² None 8. In the figure PQ and AB are the two arcs of the concentric circles of radii 7cm and 3.5cm resp. with the centre O. If ∠POQ=30° , then find the area of shaded region. Topic: Areas of Sectors a Circle 7.625 cm² 8.625 cm² 9.625 cm² 9.815 cm² None 9. A sector of circle of radius 10.5 cm is give below. Find its perimeter. ( Take π=$\displaystyle \dfrac{22}{7}$) Topic: Perimeter of Sectors 36 cm 32 cm 45 cm 48 cm None 10. The long and short hands of a clock are 6 cm and 4 cm long respectively. Find the sum of the distances travelled by their tips in 24 hours. (Use π=3⋅14 ) Topic: Circumference and Distance Travelled 354.56 cm 654.56 cm 954.56 cm 284.56 cm None 11. A car has two wipers which do not overlap. Each wiper has a blade of length 21 cm sweeping through an angle 120°. Find the total area cleaned at each sweep of the blades. (Take π=22/7) Topic: Properties of Area 634 cm² 894 cm² 924 cm² 874 cm² None 12. Find the area of a sector of a circle with radius 6 cm and angle of the sector as 60°. Topic: Areas of Sectors a Circle $\displaystyle \dfrac{102}{7}$ cm² $\displaystyle \dfrac{132}{7}$ cm² $\displaystyle \dfrac{154}{7}$ cm² $\displaystyle \dfrac{22}{7}$ cm² None 13. Find the area of a quadrant of a circle whose circumference is 22 cm. Topic: Area and Quadrant of a Circle $\displaystyle \dfrac{77}{8}$ cm² $\displaystyle \dfrac{65}{8}$ cm² $\displaystyle \dfrac{52}{3}$ cm² $\displaystyle \dfrac{72}{4}$ cm² None 14. The length of the minute hand of a clock is 14 cm. Find the area swept by it in 5 minutes. Topic: Properties of Area $\displaystyle \dfrac{365}{2}$ sq.cm $\displaystyle \dfrac{147}{9}$ sq.cm $\displaystyle \dfrac{247}{8}$ sq.cm $\displaystyle \dfrac{154}{3}$ sq.cm None 15. The area of the minor segment of a circle of radius 14 cm, when its central angle is 60°. [Useπ= $\displaystyle \dfrac{22}{7}$ ] Topic: Areas of Segments 11.29 cm² 17.89 cm² 15.56 cm² 63.69 cm² None 16. A wire is looped in the form of a circle of radius 28 cm. It is rebent into a square form. Determine the length of the side of the square. Topic: Conversion of Wire Shapes 44 cm 54 cm 25 cm 36 cm None 17. An umbrella has 8 ribs which are equally spaced (as shown in the figure). Assuming the umbrella to be a flat circle of radius 42 cm, find the area between the two consecutive ribs of the umbrella. Topic: Areas Between Ribs in a Circle 365 cm² 568 cm² 693 cm² 254 cm² None 18. To warn ships for underwater rocks, a lighthouse spreads a redcoloured light over a sector of angle 72 ∘ to a distance of 15 km. Find the area of the sea over which the ships are warned. [Use π=3.14] Topic: Areas of Sectors a Circle 141.3 km² 142.2 km² 356.1 km² 253.2 km² None 19. Find the area of a right-angled triangle, if the radius of its circumcircle is 7.5 cm and the altitude drawn to the hypotenuse is 6 cm long. Topic: Area of Triangle Using Circumcircle 75 cm² 65 cm² 25 cm² 45 cm² None 20. The length of a chain used as the boundary of the semi-circular park is 90 cm. Find the area of the park. Topic: Area of Semi-Circular 961.95 cm² 361.36 cm² 481.25 cm² 471.25 cm² None 21. A sector is cut from a circle of radius 21 cm. The angle of the sector is 150°. What will be the length of its arc and area? Topic: Arc Length and Sector Area 577.5 cm² ,55 cm 895.5 cm² ,56 cm 546.5 cm² ,96 cm 564.5 cm² ,26 cm None 22. A pendulum moving through an angle of 30° and describes an arc 4.4 cm in length. Find the length of the pendulum. Topic: Arc Length 8.4 cm 8.0 cm 9.4 cm 6.4 cm None 23. If the difference between the circumference and the radius of a circle is 37 cm, then using π=$\displaystyle \dfrac{22}{7}$ , find the radius of the circle (in cm). Topic: Circumference and Radius 7 14 44 124 None 24. What is the area of a sector of a circle with radius 6 cm if angle of the sector is 60°? Topic: Areas of Sectors a Circle $\displaystyle \dfrac{132}{7}$ cm² $\displaystyle \dfrac{154}{7}$ cm² $\displaystyle \dfrac{365}{7}$ cm² $\displaystyle \dfrac{248}{7}$ cm² None 25. What is the area of a quadrant of a circle whose circumference is 22 cm? Topic: Area and Quadrant of a Circle $ \displaystyle \dfrac{99}{8}$ cm² $ \displaystyle \dfrac{88}{8}$ cm² $ \displaystyle \dfrac{77}{8}$ cm² $ \displaystyle \dfrac{57}{4}$ cm² None 26. A blacksmith Rajesh bent a steel wire, in the form of a square, encloses an area of 121sq cm. The same wire he bent in the form of a circle, then the area of the circle is: Topic: Area of Circle from Perimeter 154 cm² 256 cm² 365 cm² 124 cm² None 27. The diameter of a circular pond is 17.5 m. If is surrounded by a path of width 3.5 m, then the area of the path is: Topic: Area of a Circle Using Diameters 145 m² 235 m² 231 m² 241 m² None 28. The area and perimeter of a sector of a circle with radius 6 cm if angle of the sector is 60° is: Topic: Area and Perimeter of a Sector 63.63 cm² ,88.28 cm 56.86 cm² ,56.28 cm 18.86 cm² ,18.28 cm 4586 cm² ,15.28 cm None 29. Flowers are to be planted in the shaded portion which is shown by sectors of two concentric circles of radii 7 m and 3.5 m, then the area of the shaded region is: (Use π= $\displaystyle \dfrac{22}{7}$ ) Topic: Area of Concentric Circles 3.625 cm² 9.625 cm² 8.235 cm² 3.525 cm² None 30. The radius of a circle is 14 cm and the area of the sector is filled with water is 102.7 cm² , then the central angle of the sector is: Topic: Central Angle of a Sector 30° 120° 90° 60° None 31. In a circle of radius 21 cm, an arc subtends an angle of 60 ∘ at the centre, then the length of the arc and the area of the sector is: Topic: Arc Length and Sector Area 42 cm, 891 cm² 56 cm, 569 cm² 44 cm, 631 cm² 22 cm, 231 cm² None 32. In a circle of radius 21 cm, an arc subtends an angle of 60° at the centre, then the area of the minor segment is and the area of the major segment is: Topic: Area of Minor and Major Segment 78.05 cm² ,6369 cm² 52.05 cm² ,6363 cm² 50.05 cm² ,2255 cm² 40.05 cm² ,1155 cm² None 33. Find the area of shaded region in the given figure, where a circle of radius 6 cm has been drawn with vertex O of an equilateral triangle OAB of side 12 cm. (Use π=3.14 and 3 =1.73) Topic: Properties of Area 457.64 cm² 137.64 cm² 124.64 cm² 147.64 cm² None 34. If the sum of the areas of two circles with radii R1 and R2 is equal to the area of a circle of radius R, then: Topic: Areas of Circles $\displaystyle {{R}_{1} ^{2}}+{{R}_{2} ^{2}}={{R}^{2}}$ $\displaystyle {{R}_{1}}+{{R}_{{2}}}=R$ $\displaystyle {{R}_{1}}+{{R}_{2}}={{R}^{2}}$ $\displaystyle {{R}_{1} ^{2}}+{{R}_{2} ^{2}}<{{R}^{2}}$ None 35. If the sum of the circumferences of two circles with radii $\displaystyle {{R}_{1}}$ and $\displaystyle {{R}_{2}}$ is equal to the circumference of a circle of radius R, then: Topic: Circumferences of Circles $\displaystyle {{R}_{1}}+{{R}_{2}}>R$ $\displaystyle {{R}_{1}}+{{R}_{2}}=R$ $\displaystyle {{R}_{1}}+{{R}_{2}}= 2R$ $\displaystyle {{R}_{1} ^{2}}+{{R}_{2} ^{2}}={{R}^{2}}$ None 36. Area of the largest triangle that can be inscribed in a semi-circle of radius r units is: Topic: Area of Triangle in a Semi-Circle r² sq units 2r sq units r sq units q² sq units None 37. The area of the circle that can be inscribed in a square of side 6 cm is: Topic: Circle Inscribed in a Square 9π cm² 6π cm² 18π cm² 21π cm² None 38. The perimeter of a square circumscribing a circle of radius a cm is: Topic: Square Circumscribing a Circle 4a cm 8a cm 2a cm 10a cm None 39. In the given figure, a square is inscribed in a circle of diameter d and another square is circumscribing the circle. Is the area of the outer square four times the area of the inner square? Topic: Squares Inscribed and Circumscribed in a Circle Yes No Cannot be determined Incomplete information None 40. The area of segment of a circle is less than the area of its corresponding sector? Is it true or false? Topic: Area of Segment and Sector False True Cannot be predicted Incomplete information None 1 out of 40 Time's up
Sign in with Google
Sign in with Facebook