SURFACE AND AREA

Surface Area and Volume

1.       The edges of a rectangular box are in the ratio 1 : 2 : 3 and its surface area is 88 cm². The volume of the box is

(1)  24 cm³                         (2) 48cm³                      (3) 64 cm³                               (4) 120 cm³

2.       A right triangle with sides 3 cm, 4 cm and 5 cm is rotated about the side 3 cm to form a cone, the volume of the cone, so formed is

(1)  16π cm³                       (2) 12π cm                       (3) 15π cm³                                           (4) 20π cm³

3.       If the length of each side of a regular tetrahedron is 12cm,then the volume of the tetrahedron is

(1)  144 cu. Cm.         (2) 72 cu. Cm.            (3) 8 cu. Cm                      (4)  cu. Cm

4.       Two right circular cylinders of equal volume have their heights in the ratio 1 : 2. The ratio of their radii is

(1)   : 1                          (2) 2 : 1                             (3) 1 : 2                                    (4) 1 : 4

5.       The base radii of two cylinders are in the ratio 2 : 3 and their height are in the ratio 5:3. The ratio of their volume is

(1)  27 : 20                         (2) 20.27                          (3) 9:4                                       (4) 4:9

6.       A hollow cylindrical tube 20 cm long , is made of iron and its external and internal diameters are 8 cm and 6 cm respectively. The volume of iron used in making the tube is (π = )

(1)  1760 cu. Cm.            (2) 880 cu. Cm.                 (3) 440 cu. Cm.                       (4) 220 cu. Cm.

7.       A hollow iron pipe is 21 cm long and its exterior diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weights 8 g/cm³, then the weight of the pipe is (Take π = )

(1)  3.696 kg                  (2) 3.6kg                               (3) 36kg                                   (4) 36.9kg

8.       A right circular cylinder of height 16 cm is covered by a rectangular tin foil of size

16 cm  22cm. The volume of the cylinder is

(1)  352cm³                              (2) 308cm³                             (3) 616cm³                                            (4) 176cm³

9.       The volume of the metal of a cylindrical pipe is 748 cm³. The length of the pipe is 14cm and its external radius is 9cm. Its thickness is(Take π = )

(1)  1cm                          (2) 5.2cm                               (3) 2.3cm                               (4) 3.7cm

10.    Two iron sheets each of diameter 6cm are immersed in the water contained in a cylindrical vessel of radius 6cm. The level of the water in the vessel will be raised by

(1)  1cm                          (2) 2cm                                  (3) 3cm                                   (4) 6cm

11.    The radii of the base of two cylinders A and B are in the ratio 3 : 2 and their height in the ratio n : 1. If the volume of cylinder A is 3 times that of cylinder B, the value of n is

(1)                                  (2)                                         (3)                                        (4)

12.    Water is pumped out through a circular pipe whose internal diameter is 7cm. If flow of water is 12cm per second, how many litres of water is being out in one hour?

(1)  1663.2                      (2) 1500                                (3) 1747.6                               (4) 2000

13.    A cylinder has ‘r’ as the radius of the base and h as the height , the radius of the base of another cylinder, having double the volume but the same height as that of the first cylinder must be equal to

(1)                                 (2) 2r                                      (3) r                                   (4)

14.    From a solid cylinder of height 10cm and radius of the base 6cm , a cone of same height and same base is removed. The volume of the remaining solid is :

(1)  240π cu. Cm            (2) 5280π cu. Cm                 (3) 620π cu. Cm                    (4) 360 cu. Cm

15.    The radius of a cylinder is 10cm and height is 4cm. The number of centimetres that may be added either to the radius or to the height to get the same increase in the volume of the cylinder is

(1)  5cm                           (2) 4cm                                   (3) 25cm                                 (4) 16cm

16.    The perimeter of the base of a right circular cylinder is ‘a’ unit. If the volume of the cylinder is V cubic unit, then the height of the cylinder is

(1)   unit                 (2)  unit                             (3)  unit                         (4)

17.    If diagonal of a cube is  cm, then its volume in cubic cm is :

(1)  8                              (2) 12                                         (3) 24                                     (4)

18.    If the area of the base of a cone is 770cm² and the area of the curved surface is 814cm², then its volume( in cm³) is :

(1)  213                     (2) 392                                  (3) 550                            (4) 616

19.    The radius of the base and height  of a right circular cone are in the ratio 5 : 12. If the volume of the cone is 314  cm³ , the slant height(in cm) of the cone will be

(1)  12                            (2) 13                                           (3) 15                                   (4) 17

20.    The radius of the base of a right circular cone is doubled keeping its height fixed. The volume of the cone will be

(1)  three times of the previous volume                   (2) four times of the previous volume

(3)  times of the previous volume                       (4) double of the previous volume

21.    The circumference of the base of a 16cm height solid cone is 33cm. What is the volume of the cone in cm³?

(1)  1028                      (2) 616                                           (3) 462                                (4) 828

22.    A cuboidal water tank has 216 litres of water. Its depth is  of its length and breadth is  of  of the difference of length and depth. The length of the tank is

(1)  72dm                    (2) 18dm                                        (3) 6dm                              (4) 2dm

23.    A wooden box measures 20cm by 12cm by 10cm. Thickness of wood is 1cm.Volume of wood to make the box(in cubic cm) is

(1)  960                       (2) 519                                              (3) 2400                           (4) 1120

24.    Water flows into a tank which is 200m long and 150m wide, through a pipe of cross-section 0.3m 0.2m at 20 km/hour. Then the time(in hours) for the water level in the tank to reach 8m is

(1)  50                         (2) 120                                              (3) 150                              (4) 200

25.    A rectangular sheet of metal is 40 cm by 15 cm. Equal squares of side 4cm are cut off at the corners and the remainder is folded up to form an open rectangular box. The volume of the box

(1)  896cm³                       (2) 986cm³                                                               (3) 600cm³                                  (4) 916cm³

26.    A godown is 15m long and 12m broad. The sum of the area of the floor and the ceiling is equal to the sum of areas of the four walls. The volume(in m³) of the godown is :

(1)  900                       (2) 1200                                              (3) 1800                           (4) 720

27.    If height of a given cone be doubled and radius of the base remains the same, the ratio of the volume of the given cone to that of the second cone will be

(1)  2 : 1                      (2) 1 : 8                                                (3) 1 : 2                            (4) 8 : 1

28.    Each of the measure of the radius of base of a cone and that of a sphere is 8cm. Also, the volume of these two solids are equal. The slant height of the cone is

(1)  8                       (2) 4                                            (3) 34                        (4) 34

29.    A cone of height 15cm and base diameter 30cm is carved out of a wooden sphere of radius 15cm.The percentage of wasted wood is :

(1)  75%                          (2) 50%                                               (3) 40%                          (4) 25%

30.    In a right circular cone, the radius of its base is 7cm and its height 24cm. A cross-section is made through the midpoint of the height parallel to the base. The volume of the upper portion is

(1)  169 cm³                (2) 154 cm³                                           (3) 1078 cm³               (4) 800 cm³

31.    The volume of a conical tent is 1232 cu. M and the area of its base is 154sq.m. Find the length of the canvas required to build the tent, if the canvas is 2m in width. (Take π = )

(1)  270m                         (2) 272m                                           (3) 276m                        (4) 275m

32.    A hollow spherical metallic ball has an external diameter 6cm and  cm thick. The volume of the ball (in cm³) is (Take π = )

(1)  41                             (2) 37                                                (3) 47                          (4) 40

33.    If  the radius of a sphere is doubled. Its volume becomes

(1)  double                      (2) four times                                   (3)  Six times                (4) eight times

34.    The total surface area of a solid hemisphere is 108π cm². The volume of the hemisphere is

(1)  72π cm³                    (2) 144π cm³                                     (3) 108 cm³             (4) 54 cm³

35.    The largest sphere is carved out of a cube of side 7cm. The volume of the sphere

 (in cm³) will be

(1)  718.66                        (2) 543.72                                        (3) 481.34                     (4) 179.67

36.    There is a pyramid on a base which is a regular hexagon of side 2a cm. If every slant edge of this pyramid is of lengh  cm, then the volume of this pyramid is

(1)  3a³ cm³                       (2) 3a³ cm³                                 (3) 3a³ cm³              (4) 6a³

37.    The base of a right prism is a trapezium. The length of the parallel sides are 8cm and 14cm and the distance between the parallel sides is 8cm. If the volume of the prism is 1056 cm³, then the height of the prism is

(1)  44cm                           (2) 16.5cm                                        (3) 12cm                     (4) 10.56cm

38.    The base of a right prism is an equilateral triangle of side 8cm and height of the prism is 10cm. Then the volume of the prism is

(1)  320 cu cm            (2) 160 cu cm                              (3) 150 cu cm       (4) 300 cu cm

39.    The diameter of the moon is assumed to be one fourth of the diameter of the earth. Then the ratio of the volume of the earth to that of the moon is

(1)  64 : 1                          (2) 1 : 64                                             (3) 60 : 7                     (4) 7 : 60

40.    A conical vessel whose internal radius is 12 cm and height 50 cm is full of liquid. The contents are emptied into a cylindrical vessel with radius(internal) 1ocm. The height to which the liquid rise in the cylindrical vessel is

(1)  25cm                         (2) 20cm                                             (3) 24cm                     (4) 22cm

41.    The total surface area of a cube and a sphere are equal. What will be the ratio between their volume?

(1)  π : 6                          (2)  :                                      (3)  :                  (4) 6 : π

42.    The ratio of the volume of a cube to that of a sphere, which will fit exactly inside the cube, is

(1)   π : 6                         (2) 6 : π                                                    (3) 3 : π                       (4) π: 3

43.    The size of  a rectangular piece of paper is 100cm 44cm. A cylinder is formed by rolling the paper along its length. The volume of the cylinder is  (Take π = )

(1)  4400cm³                  (2) 15400cm³                             (3) 35000 cm³                         (4) 144 cm³

44.    A solid wooden toy is in the shape of a right circular cone mounted on a hemisphere. If the radius of the hemisphere is 4.2 cm and the total heidht of the toy is 10.2cm , find the volume of the wooden toy(nearly),

(1)  104 cm³                             (2) 162cm³                               (3) 427 cm³                 (4) 266 cm³

45.    From a right circular cylinder of radius 10cm and height 21cm, a right circular cone of same base-radius is removed. If the volume of the remaining portion is 4400 cm³, then the height of the removed cone (Take π = )

(1)  15cm                        (2) 18cm                                     (3) 21cm                     (4) 24cm

46.    If a solid cone of volume 27 π cm³ is kept inside a hollow cylinder whose radius and height are that of the cone, then the volume of water needed to empty space is

(1)  3 π cm³                   (2) 18π cm³                                 (3) 54 π cm³             (4) 81 π cm³ 

47.    The volume of a cylinder and a cone are in the ratio 3 : 1. Find their diameters and then compare them when their heights are equal.

(1)  Diameter of cylinder = 2 times of diameter of cone

(2)  Diameter of cylinder = diameter of cone

(3)  Diameter of cylinder ˃ diameter of cone

(4)  Diameter of cylinder < diameter of cone

48.    If the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, the volume will be decreased by

(1)  0%                           (2) 25%                                        (3) 62.5%                  (4) 75%

49.    A solid metallic spherical ball of diameter 6cm is melted and recasted into a cone with diameter of the base as 12cm. The height of the cone is

(1)  6cm                         (2) 2cm                                        (3) 4cm                     (4) 3cm

50.    The radius of cross-section of a solid cylindrical rod of iron is 50cm.The cylinder is melted down and formed into 6 solid spherical balls of the same radius as that of the cylinder. The length of the rod(in meters) is

(1)  0.8                           (2) 2                                               (3) 3                          (4) 4

51.    Two right circular cones of equal height of radii of base 3cm and 4cm are melted together and made to a solid sphere of radius 5cm. The height of a cone is

(1)  10cm                     (2) 20cm                                     (3) 30cm                   (4) 40cm

52.    A sphere is cut into two hemispheres. One of them is used as bowl. It takes 8 bowlfuls of this to fill a conical vessel of height 12cm and radius 6cm.The radius of the sphere (in cm) will be

(1)  3                                   (2) 2                                    (3) 4                                 (4) 6

53.    Some bricks are arranged in an are measuring 20cu cm. If the length, breadth and height of each brick is 25cm, 12.5cm and 8cm respectively, then in thet pile the number of bricks are(suppose there is no gap in between two bricks)

(1)  6,000                         (2) 8,000                            (3) 4,000                        (4) 10,000

54.    Each edge of a tetrahedron is 4cm. Its volume(in cu cm) is

(1)                           (2) 16                                        (3)                           (4) 16

55.    A hemisphere bowl of internal radius 15cm contains liquid. The liquid is to be filled into cylindrical shaped bottles of diameter 5cm and height 6cm. The number of bottles required to empty the bowl is

(1)  30                            (2) 40                                 (3) 50                              (4) 60

56.    The height of a circular cylinder is increased six times and the base area is decreased to one-ninth of its value. The factor by which the lateral surface of the cylinder increases is

(1)  2                              (2)                                  (3)                                 (4)  

57.    Find the length of the largest rod that can be placed in a room 16m long, 12m broad and 10m high

(1)  23m                        (2) 68m                             (3) 22 m                      (4) 22m

58.    The perimeter of the floor of a room is 18m. What is the area of the walls of the room, if the height of the room is 3m?

(1)  21m²                     (2) 42 m²                                             (3) 54 m²                        (4) 108 m²

59.    The height and the radius of the base of a right circular cone are 12cm and 6cm respectively. The radius of the circular cross-section of te cone cut by a plane parallel to its base at a distance of 3cm from the base is

(1)  4cm                      (2) 5.5cm                           (3) 4.5cm                      (4) 3.5cm

60.    A semi-circular sheet of metal of diameter 28cm is bent into an open conical cup. The depth of the cup is approximately

(1)  11cm                   (2) 12cm                            (3) 13cm                          (4) 14cm

61.    If h, c, v are respectively the height, curved surface area and volume of a right circular cone, then the value of 3 πvh³ – c²h² + 9v² is

(1)  2                          (2) -1                                      (3) 1                                  (4) 0

62.    The ratio of the length and breadth of a ractanglular parallelepiped is 5 : 3 and its height is 6cm. If the total surface area of the parallelepiped be 558sq. Cm. Then its length in dm is

(1)  9                                 (2) 1.5                                   (3) 10                                (4) 15

63.    A cuboidal block 6cm 9cm   12cm is cut up into exact number of equal cubes. The least possible number of cubes will be

(1)  6                                 (2) 9                                         (3) 24                               (4) 30

64.    The cost of carpeting a room is Rs.120. If the width had been 4m less, the cost of carpet would have been Rs. 20 less. The width of the room is

(1)  24m                              (2) 20m                              (3) 25m                             (4) 18.5m

65.    If the arcs of square length in two circles subtend angles of 60⁰ and 70⁰ at their centres, the ratio of their radii is

(1)  3 : 4                         (2) 4 : 5                               (3) 5 : 4                             (4) 3 : 5

66.    In an equilateral triangle ABC of side 10cm, the side BC is trisected at D. Then the length (in cm) of AD is

(1)  3                         (2) 7                            (3)                              (4)

67.    The length of one side of rhombus is 6.5cm and its altitude is 10cm. If the length of its diagonal be 26cm , the length of the other diagonal will be

(1)  5cm                             (2) 10cm                                    (3) 6.5cm                       (4) 26 cm

68.    Each interior angle of a regular polygon is 18⁰ more than eight times an exterior angle. The number of sides of the polygon is

(1)  10                                  (2) 15                                 (3) 20                                 (4) 25

69.    A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1m and its walls are 5cm thick. The thickness of the bottom

(1)  1m                              (2) 1.1m                                     (3) 1dm                          (4) 90cm

70.    A circle is inscribed in a square. An equilateral triangle of side 4 cm is inscribed in that circle. The length of the diagonal of the square (in cm) is

(1)   4                                (2) 8                                  (3) 8                           (4) 16

71.    The rain water from a roof 22m20m drains into a cylindrical vessel having a diameter of 2m and height 3.5m. If the vessel is just full, then the rainfall(in cm) is :

(1)  2                                    (2) 2.5                                 (3) 3                                 (4) 4.5

72.    An elephant of length 4m is at one corner of a rectangular cage of size 16m30m and faces towards the diagonally opposite corner. If the elephant starts moving towards the diagonally opposite corner it takes 15 sec to reach this corner. Find the speed of the elephant

(1)  1                 (2) 2               (3) 1.87             (4) 1.5

73.    A plate on square base made of brass is of length x cm and width 1mm. The plate weights 4725 gm. If 1 cubic cm of brass weighs 8.4 gm, then the value of x is

(1)  75                            (2) 76                          (3) 72                               (4) 74

74.    The paint in a certain container is sufficient to paint an area equal to 6.375 m². How many bricks measuring 22.5 cm by 10 cm by 7.5 cm can be painted out of this container?

(1) 200                     (2) 1000                     (3) 10                     (4) 100                         (5) None of these