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MENSURATION CSAT_ QUESTION

1. The perimeter of a rectangle of 4 cm breadth 7. The perimeter of a square and a circular field
is 32 cm. Find the area of the rectangle. are the same. If the area of the square is 1936
(A) 32 (B) 24 m2. What is the area of the circular field?
(C) 48 (D) 96 (A) 2008 (B) 2116
(C) 2464 (D) 1928
2. If the length the diagonal of a square is 5 cm
then what will be the area of the square? 8. The perimeter of a rectangle is 200 cm and
25 27 the difference of two sides is 36 cm. Find the
(A) (B) length of the rectangle.
4 4
26 (A) 68 (B) 96
(C) 9 (D)
3 (C) 32 (D) 64

3. If the radius of a circle is increased by 3 cm 9. A wire when bent in the form of square
then area of the circle increases by 198 cm2 , encloses an area of 4356 cm2. What will be
find the original radius of the circle. the enclosed area when the same wire is bent
(A) 10 (B) 6 into the form of a circle?

(C) 7 (D) 9 (A) 5775 (B) 6238

(C) 5544 (D) 2739

4. What is the area of a circle of circumference

44 cm? 10. Find the length of the longest rod that can be
placed in a hall of 12 m length, 12 m breadth
(A) 154 (B) 216
and 6 m height.
(C) 616 (D) 96 (A) 16 (B) 12
(C) 9 (D) 18
5. The length of a rectanglular hall is five-fourth
of its breadth. If area of the floor is 845 cm2
11. The difference of the area of two squares
then find the difference between length and drawn on two line segments of different
breadth of the hall. lengths is 80 sq. cm, find the length of the
(A) 5.5 (B) 4.275 greater line segment if one is longer than the
other by 4 cm.
(C) 3.25 (D) 6.5 (A) 12 (B) 8
(C) 9 (D) 10
6. The perimeter of two squares are 16 and 20
cm. The perimeter of a third square whose 12. There is a rectangular tank of length 150 m
area is equal to the sum of the areas of these and breadth 120 m in a circular field. If the
squares is: area of the land portion of the field is 7600
m2, what is the radius of the field?
(A) 2 22 (B) 4 41
(A) 92.32 (B) 98.67
(C) 4 39 (D) 4 11 (C) 90.25 (D) 100.5
13. If the length and breadth of a rectangle are in Directions (21-22): Read the following statement and
the ratio 5:3 and its perimeter is 48 cm, then answer the following questions.
find the area of the rectangle. A wire when bent in the form of a square, encloses
(A) 125 (B) 135 an area 324 cm2. The same wire is bent into the form
(C) 215 (D) 225 of a semicircle.

14. A path of uniform width runs round the inside 21. Find the radius of the semicircle.
of a rectangular field 20 cm long and 18cm (A) 14 cm (B) 7 cm
wide . If the path occupies 136 cm2. then find (C) 20 cm (D) 21 cm
the width of the path.
(A) 17 (B) 2
22. Find the area of the semicircle.
(C) 14 (D) 6
(A) 215 cm2 (B) 308 cm2
(C) 154 cm2 (D) 314 cm2
15. Find the area of a square inscribed in a circle
of radius 5 cm.
Directions (23-24): Read the following statement and
(A) 80 (B)75
answer the questions given below.
(C) 50 (D) 100
The area of a circle is 346.5 cm2.

16. The diameter of a wheel is 42 cm. What is the

23. Find the radius of the circle.
distance travelled by it in 11 revolutions?
(A) 14 cm (B) 10 cm
(A) 1636 cm (B) 1452 cm
(C) 21 cm (D)10.5 cm
(C) 1236 cm (D) 1537 cm
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24. Find the cirumference of the circle.

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17. What is the area of the greatest circle inside a

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(A) 44 (B) 22
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square of side 35 cm?

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(A) 379.6 cm2 (B) 950.8 cm2 (C) 66 (D) 33

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2 2
(C) 864.6 cm (D) 962.5 cm
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25. The radii of two circles are 7 cm and 24 cm.

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Find the radius of a circle whose area is the

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18. What are the number of revolutions a wheel

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of diameter 20 cm makes in travelling a sum of the area of these two circles.

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distance of 132 m.
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(A) 25 (B)30
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(A) 170 (B) 210 (C) 32 (D) 36

(C) 240 (D) 360

Directions (26-30): Read the following statement and

19. Find the radius of a wheel that makes 875
answer the questions given below.
revolutions to go 16.5 km.
(A) 4 m (B) 2 m A wire of length 132 cm is first bent to form a circle
(C) 3 m (D) 6 m and then rebent to form a square.

20. If the difference between circumference and

diameter of a circle is 60 cm then find the 26. Find the radius of the circle .
radius of the circle. (A) 12 cm (B)10.5 cm
(A) 7 cm (B) 14 cm
(C) 14 cm (D) 21 cm
(C) 21 cm (D) 35 cm
27. Find the area of the circle. 35. The ratio of the length of the parallel sides of
(A) 1288 (B) 1208 a trapezium is 5:3. The shortest distance
between then is 18 cm. If the area of the
(C) 1386 (D) 1296
trapezium is 360 cm2 then find the difference
of the lenth of the parallel sides.
28. Find the length of the side of the square.
(A) 15 (B) 12
(A) 33 (B) 22
(C) 10 (D) 20
(C) 36 (D) 35

36. The length of two paralles sides of a

29. Find the area of the square. trapezium are 10 cm and 20 cm. If its area is
(A) 1386 (B) 1089 285 sq cm then find the height of the
trapezium.
(C) 1296 (D) 1398
(A) 19 (B) 20
(C) 18 (D) 16
30. What is the difference of the two enclosed
area?
37. The floor of a hall is 50 m long and 10 m wide.
(A) 296 (B)297 Find the cost of covering the floor with carpet
(C) 172 (D)178 50 cm wide at the rate of Rs. 20 per meter.
(A) 17250 (B)18750
(C) 15750 (D) 20,000
31. The outer and inner circumference of a
circular path be 176 cm and 132 cm
respectively. Find the area of the path. 38. The outer circumference of a circular path is
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572 m. The width of the path is 7 m. What is

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(A) 1127 (B) 1296

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the cost of levelling the path at the rate of Rs.

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(C) 1078 (D) 1089 5/ ?

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(A) 20000 (B) 15000

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32. The outer and inner diameter of a circular (C) 12750 (D) 19250
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path be 128 cm and 112 cm respectively.

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What is the breadth of the path?

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39. Find the ratio of area of a square to that of

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(A) 12 (B) 4 the square drawn on its diagonal.

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(A) 1:2 (B)1:3

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(C) 8 (D) 6
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(C) 2:3 (D) 3:4

33. Find the area of a circle whose radius is the

40. Find the ratio of area of a square to that of an
diagonal of a square whose area is 32 cm.
equilateral triangle drawn on the diagonal.
(A) 64π (B) 36π
(A) 1: 3 (B) 3:4
(C) 35π (D) 40π
(C) 2: 3 (D) 2:1

34. What is the area of a rhombus whose

41. A circle and a square have equal
perimeter is 116 cm and one of its diagonal is
circumference. What is the ratio of the area
40 cm.
of circle and area of the square?
(A) 896 (B) 840
(A) π:1 (B) 2:1
(C) 825 (D) 876 (C) 4: π (D) π:2
Direction(42-43): Answer the following questions on 49. The length, breadth and height of a room is
the basis of the statement given below: 15 m, 12 m and 9 m respectively. Find the
The ratio of the radii of two wheels is 4:5. length of the largest bamboo that can be kept
inside the room.

42. What is the ratio of the circumference of both (A) 5 10 (B) 2 5

wheels? (C) 10 5 (D) 6 5
(A) 1:2 (B) 3:5
(C) 4:3 (D) 4:5 50. A cuboidal block of 6 cm× 12 cm×15 cm is cut
into exact number of equal cubes. Find the
43. What is the ratio of area of both the wheels? least possible number of cubes.
(A) 9:16 (B) 16:25 (A) 10 (B) 100
(C) 4:5 (D) 9:25 (C) 40 (D) 60

44. If the circumference of a circle decreased 51. The perimeter of the base of a right circular
from 4π to 2π, what change occurs in its cone is 10 cm. If height of the cone is 35 cm
area? then find the volume of the cone.
(A) halred (B) daubles 875 875
(A) (B)
(C) quadruples (D) decreased by 75% 3 6

825 825
(C) (D)
45. If the length of a rectangle is decreased by 4 6
20% and breadth is increase by 25% then area
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of rectangle:
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52. Find the volume of a right circular cylinder

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(A) remains unchanged

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whose height is 25 cm and circumference of

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(B) decreased by 2%
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its base is 44 cm.

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(C) increased by 5% (A) 3225 (B) 3850

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(D) decreased by 5%
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(C) 3625 (D) 3600

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53. A cylinder of diameter 28 cm is full of water.

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46. The length of rectangle is increased by 50% by If 22 litres of water is drawn off then find the
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what percent would the breadth be decrease in water level in the cylinder.
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decreased to keep area same?

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10 7
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(A) 35 (B) 36
(A) 33.33% (B) 16.67% 14 13
(C) 67.67% (D) 50%
5 7
(C) 32 (D) 31
6 8
47. If each side of a square is increased by 20%
then its area will increase by what percent? Direction (54-57): Answer the following questions on
(A) 78% (B) 26% the basis of the statement given below.
(C) 36% (D) 44% The area of the four walls of a room is 800 m2 and its
length is thrice its breadth. Its height is 10 m.

48. If the diagonal of a cube is 48 cm then find

54. What is the area of the floor?
its volume.
(A) 225 (B) 200
(A) 36 (B) 8
(C) 4 (D) 64 (C) 250 (D) 300
55. Find the total surface area of the room. 62. Find the total surface area of the conical
(A) 1200 (B) 1400 vessel.
(C) 1500 (D) 1225 (A) 704 (B) 656
(C) 440 (D) 436
56. Find the volume occupied by the room.
(A) 3600 (B) 2500 63. Find the cost of painting this vessel from
outside at the rate of Rs. 28 per sq. cm.
(C) 3000 (D) 300
(A) 15400 (B) 7500
(C) 12300 (D) 15600
57. Two cubes of sides 3 cm each are kept side to
form a rectangular parallelopiped. Find the
total surface area of the parallelopiped. 64. A solid metallic cone of height 16 cm, radius
(A) 180 (B) 60 of base 20 cm is melted to make
hemispherical balls each of 4 cm radius. How
(C) 90 (D) 45
many such salls can be made?
(A) 25 (B) 36
Direction (58-59): Answer the following questions on
(C) 50 (D) 40
the basis of the statement given below:
Total surface area of a cube is 54 cm2
65. Find the volume of a right circular cylinder
whose height is 10 cm and circumference of
58. What is the length of the side of the cube?
its base is 110 cm.
(A) 4 (B) 2
(A) 6575 (B) 6225
(C) 6 (D) 3
(C) 8725 (D) 9625
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59. Find the volume of the cube.

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(A) 6 (B) 9
Direction (66-67): Answer the following questions on
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(C) 18 (D) 27 the basis of the statement given below.

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The surface area of a sphere is 100π cm2.

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60. A metallic sphere is melted and recast in the

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shape of a cone with equal base radius (R) as

66 Find the diameter of the sphere.
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that of the sphere. Which of the following

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(A) 20 (B) 15
options is correct? (H is height of case)
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(C) 5 (D) 10
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(B) H  3R
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(A) H=2R

(C) H =4R (D) H  3H 67. Find the volume of the sphere.

150  250 
(A) (B)
7 3
Direction (61-63): Answer the following questions on
the basis of the statement given below: 500 
(C) 200π (D)
3
The height of a conical vessel is 24 cm and the
circumference of its base is 44 cm.
68. A hollow cylinderical tube 14 cm long is made
of iron and its external and internal diameters
61. What is the volume of conical vessel? are 16 cm and 12 cm respectively. Find the
(A) 2144 (B) 1232 volume of the iron used in making the tube.
(C) 2156 (D) 1536 (A) 1256 (B) 1296
(C) 1275 (D) 1232
69. If volume of a right circular cylinder is 49πh 75. Find the ratio of the slant height to the radius
m3, where h is the height of the cylinder then of the cone.
find the diameter of the base of the cylinder. (A) 7:15 (B) 15:8
(A) 7 (B) 14 (C) 25:7 (D) 36:25
(C) 20 (D) 21
76. Find the volume of the cone.
70. If the volume and surface area of a sphere are (A) 1256 (B) 1240
numerically same then find its radius.
(C) 1276 (D) 1232
(A) 3 (B) 6
(C) 7 (D) 8
77. Find the total surface area of the cone .
(A) 704 (B) 775
71. If volume and surface area of a cylinder are
(C) 712 (D) 776
numerically equal then find its radius.
(A) 6 (B) 4
(C) 2 (D) 8
78. The diameter of the base of a right circular
cone is 6 cm and its height is 4 cm. Find the
Direction (72-74): Answer the following questions on slant height of the cone.
the basis of the statement given below. (A) 5 (B) 10
The area of the base of a cylinder is 616 cm2 and its (C) 15 (D) 8
curved surface area is 880 cm2.
79 I: The ratio of curved surface area and total
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surface area of a cylinder is 1:3.

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72. Find the height of the cylinder.

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II: Radius of the cylinder is 2 3 cm.

(A) 5 (B) 7
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What is the height of the cylinder?

(C) 10 (D) 12
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(A) I is sufficent (B) II is sufficent

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(C) I & II (D) None

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73. Find the volume of the cylinder.

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(A) 6160 (B) 2756

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80. Find the volume of sphere

(C) 3668 (D) 3829
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I: Total surface area of sphere is 144π.

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II. Diameter of the sphere is 12 cm

74. Find the different between curved surface
area and the total surface area of the (A) I is sufficent
cylinder. (B) II is sufficent
(A) 1232 (B) 1296 (C) Not sufficent
(C) 1276 (D) 1275 (D) Either is sufficient

Direction (75-77): Answer the following questions on 81. A cap is in the form of a right circular cone of
the basis of the statement given below. base radius 12 cm and height 5 cm. Find the
area of sheet required to make one dozen
If the area of the base of a cone is 154 cm2 and its cups.
curved surface area is 550 cm2. (A) 1276π (B) 1639π
(C) 1872π (D) 1768π
82. The volume of a conical tent is 1232 cm3 and 89. If the number of sides of a regular polygon is
area of base is 616 cm2 then find radius of its 8 then find the number of diagonals .
base. (A) 18 (B) 20
(A) 14 (B) 7
(C) 16 (D) 26
(C) 16 (D) 8

90. The sum of the length breadth and depth of a

83. Find the curved surface area of the cone in
cuboid is 12 cm and its diagonal is √ cm.
question 82.
Find its surface area.
(A) 620.36 cm2 (B) 626.35 cm2
(A) 130 (B) 125
2 2
(C) 670.12 cm (D) 636.76 cm
(C) 136 (D) 124

84. The volume of two spheres are in the ratio

91. The radius of a wire is decreased to half. If
1331:729. If the sum of radius of two sphere
volume remains same, the length will
is 40 cm then find the surface area of second
increase by:
sphere.
(A) 4 times (B) doubles
(A)1377π (B) 1875π
(C) half (D) three
(C) 1296π (D) 1250π

92. A cone, a cylinder and a sphere have equal

85. Find the surface area of first sphere in
radius and volume. What is the ratio of height
question 84.
of cone, height of cylinder and radius of
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(A) 1376π (B) 1275π

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sphere?
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(C) 1936π (D) 1296π (A) 3:4:12 (B) 12:1:4

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(C) 12:4:3 (D) 3:4:6

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86. The ratio of the radii of two cylinders is 4:3

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and ratio of heights is 3:5. Find the ratio of

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93. The ratio of radii of two spheres is 2:3 then

their volumes.
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find the ratio of their volumes.

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(A) 16:7 (B) 16:15

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(A) 8:7 (B) 8:27

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(C) 15:8 (D) 2:3

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(C) 8:29 (D) 27:16

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87. The radii of a sphere and cylinder are 3 cm

94. Find the ratio of total surface areas of spheres
each. If their volumes are equal then find the
if the ratio of their radii is 3:4.
curved surface area of the cylinder.
(A) 7:16 (B) 9:7
(A) 16π (B) 24π
(C) 9:4 (D) 9:16
(C) 20π (D) 36π

95. If the ratio of surface areas of two spheres is

88. The ratio of diagonals of two squares is 4:11.
25:49 then find the ratio of their radii.
What is the ratio of their areas?
(A) 5:7 (B) 7:9
(A) 16:49 (B) 16:48
(C) 5:9 (D) 5:4
(C) 16:11 (D) 16:121
Direction (96-98): Read the statement and answer 97. Find the total surface area of the cylinder.
the following questions. (A) 1876.6 (B) 1216.7

The height and radius of a cylinder are 7 cm. and 12 (C) 1433.1 (D) 1276.6
cm. respectively.
98. Find the volume of the cylinder.

96. Find the curved surface area of the cylinder. (A) 1636 (B) 1296

(A) 624 (B) 728 (C) 2178 (D) 3168

(C) 528 (D) 714

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