9th Class Mathematics Surface Areas and Volumes Question Bank

done Surface Areas and Volumes Total Questions - 25

• question_answer1)
  If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?
  A)
   4                                 done clear
  B)
  \[\frac{1}{\sqrt{2}}\]                  done clear
  C)
   2                     done clear
  D)
          \[\frac{1}{2}\]              done clear
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• question_answer2)
  A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. Find the difference between surface areas of two solids.
  A)
  \[~280\text{ }c{{m}^{2}}\]       done clear
  B)
                     \[~284\text{ }c{{m}^{2}}\]      done clear
  C)
         \[~296\text{ }c{{m}^{2}}\]                  done clear
  D)
         \[286\text{ }c{{m}^{2}}\] done clear
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• question_answer3)
  The height of a cone is equal to its base diameter. Then slant height of the cone is
  A)
  \[\sqrt{{{r}^{2}}+{{h}^{2}}}\]                      done clear
  B)
  \[r\sqrt{5}\]                    done clear
  C)
  \[h\sqrt{5}\]                   done clear
  D)
         \[rh\sqrt{5}\]                  done clear
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• question_answer4)
  The length of the longest rod that can be kept in a cuboidal room of dimensions \[10\,m\times 10\,m\times 5\,m\]is ___.
  A)
   16 m                            done clear
  B)
   10 m    done clear
  C)
          15 m                done clear
  D)
          12 m done clear
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• question_answer5)
  A hemispherical bowl is filled to the brim with a beverage. The contents of the bowl are transferred into a cylindrical vessel whose radius is 50% more than its height. If the diameter is same for both the bowl and the cylinder, then the amount of the beverage that can be poured from the bowl into the cylindrical vessel is ____.
  A)
  \[66\frac{2}{3}%\]                     done clear
  B)
  \[78\frac{1}{2}%\]         done clear
  C)
          100%               done clear
  D)
          None of these                done clear
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• question_answer6)
  If the length of diagonal of a cube is \[\sqrt{12}\,cm,\]then the volume of the cube is
  A)
  \[8\sqrt{12}\,c{{m}^{3}}\]                    done clear
  B)
  \[8\,c{{m}^{3}}\]         done clear
  C)
         \[16\sqrt{2}\,c{{m}^{3}}\]        done clear
  D)
         \[16\,c{{m}^{3}}\]                   done clear
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• question_answer7)
  The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is the value of r in terms of\[x\]?
  A)
  \[\frac{{{x}^{2}}}{2\pi }\]                               done clear
  B)
  \[\frac{x}{2\sqrt{\pi }}\] done clear
  C)
          \[\frac{\sqrt{2x}}{\pi }\] done clear
  D)
         \[\frac{x}{2\sqrt{\pi }}\]                         done clear
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• question_answer8)
  The edge of a cube is 20 cm. How many small cubes of edge 5 cm can be formed from this cube?
  A)
   4                                 done clear
  B)
   32                    done clear
  C)
   64                    done clear
  D)
          100                  done clear
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• question_answer9)
  The volume of two spheres are in the ratio 64 : 27. The difference of their surface areas, if the sum of their radii is 7 units, is ___.                       
  A)
  \[28\pi \,sq.\,\]units          done clear
  B)
   88 sq. units done clear
  C)
  \[88\pi \,sq.\] units    done clear
  D)
         \[4\pi \,sq.\] units            done clear
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• question_answer10)
  The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio of 5 : 3. The ratio of their volumes is ___.
  A)
   10 : 17                         done clear
  B)
   20 : 27 done clear
  C)
          17 : 27             done clear
  D)
          20 : 37 done clear
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• question_answer11)
  A covered wooden box has the inner measures as 115 cm, 75 cm, 35 cm and the thickness of wood is 2.5 cm. Then the volume of the wood is ____
  A)
   80000 cu. cm done clear
  B)
   82125 cu. cm done clear
  C)
   84000 cu. cm done clear
  D)
   85000 cu. cm done clear
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• question_answer12)
  A spherical ball of lead, 3 cm in diameter is melted and recast into three spherical balls. The diameter of two of these are 1.5 cm and 2 cm respectively. The diameter of the third ball is ____.
  A)
   2.66 cm                        done clear
  B)
   2.5 cm done clear
  C)
          3 cm                done clear
  D)
          3.5 cm             done clear
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• question_answer13)
  How many metres of cloth, 5 m wide, will be required to make a conical tent, the radius of whose base is 7 m and height is 24 m?
  A)
   550 m                          done clear
  B)
   168 m  done clear
  C)
          110m               done clear
  D)
          33.6 m             done clear
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• question_answer14)
  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 height of the toy is 10.2 cm, find the volume of the wooden toy.
  A)
  \[266.11\text{ }c{{m}^{3}}\]                done clear
  B)
  \[~301.12\,c{{m}^{3}}\]     done clear
  C)
         \[242.36\text{ }c{{m}^{3}}\]    done clear
  D)
         \[278.34\,c{{m}^{3}}\]        done clear
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• question_answer15)
  Water flows in a tank\[150\,m\,\times \,100\,m\] mat the base, through a pipe whose cross-section is 2 dm by 1.5 dm at the speed of 15 km per hour. In what time, will the water be 3 metres deep?
  A)
   50 hours                       done clear
  B)
   150 hours         done clear
  C)
          100 hours      done clear
  D)
          200 hours                     done clear
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• question_answer16)
  A teak wood log is first cut in the form of a cuboid of length 2.3 m, width 0.75 m and of a certain thickness. Its volume is \[1.104\text{ }{{m}^{3}}\]. How many rectangular planks of size \[2.3\text{ }m\times 0.75\text{ }m\times 0.04\text{ }m\]can be cut from the cuboid?
  A)
   16                    done clear
  B)
   64                    done clear
  C)
   68                    done clear
  D)
          4 done clear
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• question_answer17)
  How many bricks, each measuring \[25\,cm\times 11.25\text{ }cm\times 6\text{ }cm,\] will be needed to build a wall \[8\,m\,\times 6\,m\,\times 22.5\,cm?\]
  A)
   5600                            done clear
  B)
   6000    done clear
  C)
          6400                done clear
  D)
          7200 done clear
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• question_answer18)
  A circus tent is cylindrical to a height of 3 metres and conical above it. if its diameter is 105 m and the slant height of the conical portion is 53 m, calculate the length of the canvas 5 m wide to make the required tent.
  A)
   1996 m            done clear
  B)
   2096 m done clear
  C)
   1947 m            done clear
  D)
          1800 m done clear
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• question_answer19)
  A school provides milk to the students daily in a cylindrical glasses of diameter 7 cm. If the glass is filled with milk upto an height of 12 cm, then how many litres of milk is needed to serve 1600 students?
  A)
   739.2 litres                    done clear
  B)
   538 litres           done clear
  C)
          740 litres           done clear
  D)
          400 litres done clear
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• question_answer20)
  A small village, having a population of 5000, requires 75 litres of water per head per day. The village has got an overhead tank of measurement \[40\,m\times 25\,m\times 15\text{ }m.\] For how many days will the water of this tank last?
  A)
   30 days                        done clear
  B)
   32 days            done clear
  C)
          40 days            done clear
  D)
          45 days done clear
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• question_answer21)
  Match the following.

  Column-I	Column-II
  (p) A cylinder of radius 3 cm is inscribed in a sphere of radius 5 cm, then volume of cylinder is ___.	(1)\[38.5\,\,c{{m}^{3}}\]
  A conical pit of top diameter 3.5 cm is 12 cm deep, the capacity of pit is ___.	(2)\[512\text{ }c{{m}^{3}}\]
  (r) The length of a diagonal of a cube is \[8\sqrt{3}\,cm.\]then volume of cube is ___.	(3)\[~72\pi \text{ }c{{m}^{3}}\]
  (s) The capacity of a conical vessel with height 12 cm and slant height 13 cm is___.	(4)\[100\pi \,c{{m}^{3}}\]

  A)
  \[(p)\to (2);(q)\to (3);(r)\to (4);(s)\to (1)\] done clear
  B)
  \[(p)\to (1);(q)\to (3);(r)\to (2);(s)\to (4)\] done clear
  C)
  \[(p)\to (3);(q)\to (1);(r)\to (2);(s)\to (4)\] done clear
  D)
  \[(p)\to (4);(q)\to (1);(r)\to (3);(s)\to (2)\] done clear
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• question_answer22)
  A cylindrical tub of radius 12 cm contains water to a depth of 20 cm. A spherical iron ball is dropped into the tub and thus the level of the water is raised by 6.75 cm. What is the radius of the sphere?
  A)
   9 cm                            done clear
  B)
   13 cm  done clear
  C)
   11 cm              done clear
  D)
          15 cm  done clear
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• question_answer23)
  Read the statement carefully and write T for true and 'F' for false.

  (i) Volume of a cylinder is three times the volume of a cone on the same base and of same height.

  (ii) Volume of biggest sphere in cube of edge 6 cm is \[36\pi \text{ }c{{m}^{3}}.\]

  (iii) Cuboids and cubes are special forms of right prisms.

  A)

  (i)	(ii)	(iii)
  T	F	T

              done clear
  B)

  (i)	(ii)	(iii)
  T	T	T

              done clear
  C)

  (i)	(ii)	(iii)
  F	T	F

              done clear
  D)

  (i)	(ii)	(iii)
  F	T	T

  done clear
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• question_answer24)
  The internal and external radii of a hollow hemispherical bowl are 15 cm and 16 cm respectively, find the cost of painting the  owl at the rate of 35 paise per\[c{{m}^{2}},\]if

  (i) the area of the edge of the bowl is ignored.

  (ii) the area of the edge of the bowl is taken into account.

  A)

  (i)	(ii)
  Rs. 1058.20	Rs. 1092.30

              done clear
  B)

  (i)	(ii)
  Rs. 1020.50	Rs. 1045

              done clear
  C)

  (i)	(ii)
  Rs. 1092.50	Rs. 1058.20

              done clear
  D)

  (i)	(ii)
  Rs. 1086.20	Rs. 1095.2

  done clear
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• question_answer25)
  Study the statements carefully.

  Statement I: If diameter of a sphere is decreased by 25%, then its curved surface area is decreased by 43.75%.

  Statement II: Curved surface area is increased when diameter decreases.

  Which of the following options hold?
  A)
   Both Statement-I and Statement-II are true. done clear
  B)
   Statement-I is true but Statement-II is false. done clear
  C)
   Statement-I is false but Statement-II is true. done clear
  D)
   Both Statement-I and Statement-II are false. done clear
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