Area problems mcqs test 01

1. The cross-section of a canal is trapezium in shape. The canal is 12 m wide at the top and 8 m wide at
the bottom. If the area of the cross-section is 840 sq. m, the depth of the canal is:

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2. Four equal sized maximunm circular plates are cut of from a square paper sheet of area 784 m?. The
circumference of each plate is ?

3. A rectangular plot, measuring 90 meters by 50 meters is to be enclosed by wire fencing. If the poles of
the fence are kept 5 meters apart, how many poles will be needed?

4. The number of marble slabs of size 20 cm x 30 cm required to pave the floor of a square room of side
3 meters, is:

5. A courtyard 25 m long and 16 m broad is to be paved with bricks of dimensions 20 cm by 10 cm. The
total number of bricks required is:

6. A cow is tethered in the middle of a field with a 14 feet long rope. If the cow grazes 100 sq. ft per day,
then approximately what time will be taken by the cow to graze the whole field?

7. The breadth of a rectangular field is 60% of its length. If the perimeter of the field is 800 m, what is the
area of the field?

8. The length and breadth of the floor of the room are 20 feet and 10 feet respectively. Square tiles of 2
feet length of different colours are to be laid on the floor. Black tiles are laid in the first row on all sides.
f white tiles are laid in the one-third of the remaining and blue tiles in the rest, how many blue tiles will
be there?

9. Within a rectangular garden 10 m wide and 20 m long, we wish to pave a walk around the borders of
uniform width so as to leave an area of 96 ms for flowers. How wide should the walk be?

10. A powder tin has a square base with side 8 cm and height 14 cm. Another tin has a circular base with
diameter 8 cm and height 14 cm. The difference in their capacities is ?

11. The length of a rectangle is 18 cm and its breadth is 10 cm. When the length is increased to 25 cm,
what will be the breadth of the rectangle if the a tea remains the same?

12. Two cubes have volumes in the ratio 1:27. Then the ratio of the area of the face of one of the cubes
to that of the other is:

13. The perimeter of a triangle, is 30 cm and its area is 30 cm”. If the largest side measures 13 cm, then
what is the length of the smallest side of the triangle?

14. The length of a rectangle is 20% more than its breadth. What wil be the ratio of the area ofa
rectangle to that of a square whose side is equal to the breadth of the rectangle?

15. If each edge of a cube is doubled, then its volume:

16. A park square in shape has a 3 meter wide road inside it running along its sides. The area occupied
by the road is 1764 square meters. What is the perimeter along the outer edge of the road?

17. What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides
of the rectangle as base and a vertex on the opposite side of the rectangle?

18. The dimensions of a room are 10 mx 5 m. There are 2 doors and 3 windows in the room. The
dimensions of the doors are 1 mx 3 m. One window is of side 2 mx1.5 m and the other two windows
are of size 1 mx 1.5 m. The cost of painting the walls at Rs.3 per m is:

19. The cost of cultivating a square field at the rate of Rs .135 per hectare is Rs .1215. The cost of putting a fence around it at the rate of 75  paisa per meter would be?

20. A farmer wishes to start a 100 sq. m rectangular vegetable gardèn. Since he has only 30 m barbed
wire, he fences three sides of the garden letting his house compound wall at as the fourth side
fencing. The dimension of the garden is:

21. The cost of papering the four walls of a room is Rs.475. Each one of the length, breadth and height of
another room is double that of this room. The cost of papering the walls of this new room is:

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22. The cost of carpeting a room 18 m long with a carpet 75 cm wide at Rs.4.50 per meter is Rs.810. The
breadth of the room is:

23. The volumes of two cubes are in the ratio 8:27. The ratio of their surface areas is:

24. The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq.
. Find the length of the greater line segment if one is longer than the other by 2 cm.

25. The ratio between the length and the breadth.of a rectangular field is 3: 2. If only the length is
increased by 5 meters, the new area of the field will be 2600 sq. meters. What is the breadth of the
rectangular field?

26. The length of a room is 5.5 m and width is 3.75 m. Find the cost of paving the floor by slabs at the rate of Rs.800 per sq. meter.

27. The ratio between the length and the breadth of a rectangular park is 3:2. If a man cycling along the
boundary of the park at the speed of 12 Km/hr completes one round in 8 minutes, then the area of the
park (in sq.m) is:

28. A large field of 700 hectares is divided into two parts. The difference of the areas of the two parts is
one-fifth of the average of the two areas. What is the area of the smaller part in hectares?

29. The area of a field in the shape of a trapezium measures 1440 m. The perpendicular distance
between its parallel sides is 24 m. If the ratio of the parallel sides is 5:3, the length of the longer
parallel side is:

30. The radius of the cylinder is half its height and area of the inner part is 616 sq. cm. Approximately how
many liters of milk can it contain?

31. A hollow garden roller 63 cm wide with a girth of 440 cm is made of iron 4 cm thick. The volume of the
iron used is:

32. A took 15 seconds to cross a rectangular field diagonally walking at the rate of 52 m/min and B took
the same time to cross the same field along its sides walking at the rate of 68 m/min. The area of the
field is:

33. The length of a blackboard is 8 cm more than its breadth. If the length is increased by 7 cm and
breadth is decreased by 4 cm, the area remains the same. The length and breadth of the black board
in cm) will be:

34. if the volumes of two cubes are in the ratio 27 1, the ratio of their edges is:

35. X and Y are two cylinders of the same height. The base of X has diameter that is half the diameter ot
the base Y. If the height of X is doubled, the volume of X becomes:

36. he length of one pair of opposite sides of a square is increased by 5 cm on each side, the ratio of the
length and the breadth of the newly formed rectangle becomes 3: 2. What is the area of the original
Square?

37. The ratio between the radius of the base and the height of a cylinder is 2:3. If its volume is 12936
cm. Cm, the total surface area of the cylinder is:

38. 50 square stone slabs of equal size were needed to cover a floor area of 72 sq. m. The length of each
stone slab is:

39. each edge of a cube is increased by 25%, thén the percentage increase in its surface area is:

40. A Circular well with a diameter of 2 meters, is dug to a depth of 14 meters. What is the volume of the
earth dug out?

41. The curved surface of a cylindrical pillar is 264 m, and its volume is 924 m°. Find the ratio of its
diameter to its height.

42. One diagonal of a parallelogram is 70 cm and the perpendicular distance of this diagonal from either
of the outlying vertices is 27 cm. The area of the parallelogram (in sq. cm) Is ?

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43. Water flows through a cylindrical pipe of internal diameter 7 cm at 2 m per second. If the pipe is
always half full, then what is the volume of water (in liters ) discharges in 10 minutes?

44. Two right circular cylinders of equal volumes have their heights in the ratio 1:2. The ratio of their
radius is:

45. The sum of the radius of the base and the height of a solid cylinder is 37 meters. If the total surface
area of the cylinder be 1628 sq. meters, its, volume is:

46. A typist uses a sheet measuring 20 cm by 30 cm lengthwise. If a margin of 2 cm is left on each side
and a 3 cm margin on top and bottom, then percent of the page used for typing is:

47. The radius of a wire is decreased to one-third and its volume remains the same. The new length Is
how many times the original length?

48. The ratio of total surface area to lateral surface area of a cylinder whose radius is 20 cm and height 60
cm, is:

49. A rectangular room can be partitioned into two equal square rooms by a partition 7 meters long. What
is the area of the rectangular room in square meters?

50. If a parallelogram with area P, a rectangle with area R and a triangle with area T are all constructed
on the same base and all have the same altitude, then which of the following statements is false?

51. The ratio of height of a room to its semi-perimeter is 2:5. It costs Rs.260 to paper the walls of the
room with paper 50 cm wide at Rs.2 per meter allowing an area of 15 sq. m for doors and windows.
The height of the room is:

52. The height of a closed cylinder of given volume and the minimum surface area is ?

53. A rectangular park 60 m long and 40 m wide has two concrete crossroads running in the middle of the
part and rest of the park has been used as a lawn. The area of the lawn is 2109 sq. m, then what is
the width of the road?

54. 66 cubic centimeters of silver is drawn into a wire 1 mm in diameter. The length of the wire in meters
will be:

55. A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel
to length and the other parallel to breadth. The cost of gravelling the roads at 75 paisa per sq. meter
is:

56. The number of coins of radius 0.75 cm and thickness 0.2 cm to be melted to make a right circular
cylinder of height 8 cm and base radius 3 cm is:

57. Wheels of diameters 7 cm and 14 cm start rolling simultaneously from X and Y, which are 1980 cm
apart, towards each other in opposite directions. Both of them make the same number of revolutions
per second. If both of them meet after 10 seconds, the speed of the smaller wheel is:

58. The length of a rectangular plot is 60% more than its breadth. If the difference between the length and
the breadth of that rectangle is 24 cm, what is the area of that rectangle?

59. What is the least number of square tiles required to pave the floor of a room 15 m 17 cm long and 9 m
2 cm broad?

60. 2 meters broad pathway is to be constructed around a rectangular plot on the inside. The area of the
plot is 96 sq. m. The rate of construction is Rs.50 per square meter. Find the total cost of the
construction.

61. A housing society has been allotted a square piece of land measuring 2550.25 sq. m. What is the side
of the plot?

62. If the radius of the base of a right circular cylinder is halved, keeping the height same, what is the ratio
of the volume of the reduced cylinder to that of the original one?

63. The length bf a rectangular hall is 5 m more than its breadth. The area of the hall is 750 m. The
length of the hall is:

64. The volume of a right circular cylinder whose curved surface area is 2640 cm and circumference of
its base is 66 cm, is:

65. ABC is a right-angled triangle with right angle at B. If the semi-circle on AB with AB as diameter
encloses an area of 81 sq. cm and the semi-circle on BC with BC as diameter encloses an area of 36
sq. cm, then the area of the semi-circle on AC with A as diameter will be:

66. The front wheels of a wagon are 2 T feet in circumference and the rear wheels are 3 feet in
circumference. When the front wheels have made 10 more revolutions than the rear wheels, how
many feet has the wagon traveled?

67. The capacity of a cylindrical tank is 246.4 liters. If the height is 4 meters, what is the diameter of the
base?

68. A rectangular paper, when folded into two congruent parts had a perimeter of 34 cm for each part
folded along one set of sides and the same.is 38 cm when folded along the other set of sidewnats
the area of the paper?

69. A rectangular carpet has an area of 120 sq. meters and a perimeter of 46 meters. The length of its
diagonal is:

70. A can go round a circular path 8 times in 40 minutes. If the diameter of the circle is increased to 10
times the original diameter, then the. time.required by A to go round the new path once, traveling at the
same speed as before, is:

71. Two cylindrical vessels with radius 15 cm and 10 cm and heights 35 cm and 15 cm respectively are
filled with water. If this water is poured into a cylindrical vessel 15 cm in height, then the radius of the
vessel is:

72. if the length and breadth of a rectangular room are each increased by 1 m, then the area of floor is
increased by 21 sq. m. If the length is increased by 1 m and breadth.is decreased by 1 m, then the
area is decreased by 5 sq. m, The perimeter of the floor is:

73. The cost of fencing a square field@ Rs.20 per meter is Rs.10080. How much will it cost to lay a three
meter wide pavement along the fencing inside the field @Rs.50 per sq. meter?

74. The radius of two cylinders are in the ratio of 2 3 and their heights are in the ratio of 5: 3. The ratio of
their volumes is:

75. The périmeters of five squares are 24 cm, 32 cm, 40 cm, 76 cm and 80 cm respectively. The
perimeter of another square equal in area to the sum of the areas of these squares is: