9th Class Mathematics Surface Areas and Volumes Question Bank

done Surface Areas and Volume Total Questions - 40

• question_answer1)
  A parallelogram and a rhombus are equal in area. The diagonals of the rhombus measure 60 m 22 m. If side of a parallelogram is \[\frac{\mathbf{3}}{\mathbf{4}}\] of longer diagonals of the rhombus then altitude from the given base of the parallelogram is _________
  A)
   15 m                done clear
  B)
                                13 m      done clear
  C)
     1233 m  done clear
  D)
                                                        14.67 m done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer2)
  The length of the longest pole that can be put in a room of dimensions \[(\mathbf{12}\text{ }\mathbf{ft}\text{ }\times \text{ }\mathbf{9}\text{ }\mathbf{ft}\text{ }\times \text{ }\mathbf{8}\text{ }\mathbf{ft})\]is
  A)
   18 ft                                                                 done clear
  B)
   9 ft          done clear
  C)
   15 ft                                                                 done clear
  D)
   17 ft done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer3)
  Which among the following statements is not true?
  A)
   The volume of a sphere of radius V is equal to one third of the volume of a cylinder of radius V whose height is equal to double the diameter of the sphere. done clear
  B)
   If A solid sphere of side 'a' is converted into a cone having its radius equals to the side of the cube, then the height of the cone is twice to its diameter. done clear
  C)
   If diagonal of a cube is 9 m then volume of the cube will be \[81{{m}^{3}}\]. done clear
  D)
   All the above done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer4)
  If side of the cube is increased by 300 % then its surface area will increase by ___________
  A)
   12 times          done clear
  B)
   13 times done clear
  C)
   14 times                                               done clear
  D)
   15 times               done clear
  E)
   None of these done clear
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• question_answer5)
  A right angled triangle whose base is 21 cm and height is 20 cm, is made to turn round on the longer side. If the volume of the solid, thus generated V and the curved surface area is S, then __________
  A)
   \[V=9240\text{ }c{{m}^{3}},\text{ }S=1914\text{ }c{{m}^{2}}\]    done clear
  B)
   \[V=8820\text{ }c{{m}^{3}},\text{ }S=1885\text{ }c{{m}^{2}}\] done clear
  C)
   \[V=3820\text{ }c{{m}^{3}},\text{ }S=1685\text{ }c{{m}^{2}}\] done clear
  D)
   \[V=8240\text{ }c{{m}^{3}},\text{ }S=1734c{{m}^{2}}\] done clear
  E)
   None of these done clear
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• question_answer6)
  Two cones have their heights in the ratio 2 : 3 and the radii of their bases are in the ratio 3 : 2, then the ratio of their volumes is _________
  A)
   3 : 2         done clear
  B)
                                                        1 : 2     done clear
  C)
         1 : 3       done clear
  D)
                                                        4 : 1 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer7)
  The volume of the largest right circular cone which can be fitted in a cube whose side is '3a' equals to _________
  A)
   \[\frac{1}{8}\] of volume of a hemisphere of radius 'a' done clear
  B)
   \[\frac{27}{8}\]of volume of sphere of radius 'a'. done clear
  C)
   \[\frac{27}{16}\]of volume of sphere of radius '2a'. done clear
  D)
   \[\frac{27}{8}\]of volume of hemisphere of radius 'a' done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer8)
  Which one among the following statements is true?
  A)
   A cylinder, A hemisphere and a cone stand on equal and the same height. The ratio of their volumes is 3 : 1 : 2 respectively. done clear
  B)
    If a sphere is inscribed in a cube, then the ratio of the volume of the sphere to the volume of cube is 6 : n. done clear
  C)
   If the radius of a cylinder is tripled and height is doubled then, the volume will be 18 times of the previous. done clear
  D)
   All the above done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer9)
  The circumradius of the triangle having its sides 11 cm, 60 cm and 61 cm is R. Find the Area of this circle, \[\left( Use\text{ }\pi \frac{22}{7} \right)\text{       }\]
  A)
   \[11694.57\,c{{m}^{2}}\]        done clear
  B)
   \[12384.85\,c{{m}^{2}}\] done clear
  C)
   \[9694.57\,c{{m}^{2}}\]                                              done clear
  D)
   \[13964.29\,c{{m}^{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer10)
  Two circles touch each other externally. The sum of there areas is \[274\text{ }\pi \text{c}{{\text{m}}^{\text{2}}}\]. The distance between their centres is 22 cm. Find the difference in their radii.
  A)
   8 cm                done clear
  B)
   10 cm       done clear
  C)
   15 cm                                                              done clear
  D)
   7 cm done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer11)
  Find the area of the shaded region where each circle is of radius 7 cm as shown in the figure.
  A)
   \[126\,c{{m}^{2}}\]                                        done clear
  B)
   \[252\,c{{m}^{2}}\]      done clear
  C)
   \[342\,c{{m}^{2}}\]                                                                done clear
  D)
   \[378\,c{{m}^{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer12)
  The length of an hour hand clock is 9 cm. The area covered by it from 9 : 20 am to 10 : 00 am is _________
  A)
   \[14.143\,c{{m}^{2}}\]            done clear
  B)
   \[12.362\,c{{m}^{2}}\]    done clear
  C)
   \[13.263\,c{{m}^{2}}\]                                                done clear
  D)
   \[10.285\,c{{m}^{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer13)
  The external length, breadth and height of a closed rectangular wooder box are 20 cm, 16 cm and 8 cm respectively. The weight of the box, when is empty, is 13 kg and when it is filled with sand, is 72 kg. If it is given that thickness of the wood is - cm, then the weights of one cubic cm of wood and cubic cm of sand are respectively ________
  A)
   \[\frac{13}{265}kg\text{ and }\frac{59}{995}kg\]                                    done clear
  B)
   \[\frac{13}{565}kg\text{ and }\frac{59}{1995}kg\] done clear
  C)
   \[\frac{13}{365}kg\text{ and }\frac{419}{1495}kg\]                                 done clear
  D)
   \[\frac{13}{1565}kg\text{ and }\frac{72}{1995}kg\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer14)
  A solid cylinder has total surface area of 1848 square cm. Its curved surface area is one third of its total surface area. If a hemisphere is formed from this cylinder, then the radius (in cm) of this hemisphere is __________
  A)
   5                                                                     done clear
  B)
   \[{{7}^{3}}\sqrt{6}\] done clear
  C)
   \[{{14}^{3}}\sqrt{6}\]                                                 done clear
  D)
   \[17\sqrt{6}\] done clear
  E)
   None of these done clear
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• question_answer15)
  The curved surface area of a hemisphere of radius 6 cm is equal to \[\frac{2}{5}\] of the curved surface area of a cone of radius 12 cm. Find the volume of the cone.
  A)
  \[1357\text{ }71\,c{{m}^{3}}\] done clear
  B)
                                \[102238\,c{{m}^{3}}\] done clear
  C)
  \[1252.61\,c{{m}^{3}}\]                                               done clear
  D)
   \[2039.68\,c{{m}^{3}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer16)
  If the radius of a sphere is increased by 40 %, then its volume will be increased by _________
  A)
   74%                                                                 done clear
  B)
   74.4%        done clear
  C)
   174.4%     done clear
  D)
   80% done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer17)
  If the length of a cuboid is increased by 30%, breadth is increased by 40% and height is increased by 50% then its volume will be increased by ___________
  A)
   173%         done clear
  B)
   273%        done clear
  C)
   163%                                                   done clear
  D)
   263% done clear
  E)
   None of these done clear
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• question_answer18)
  In an event, laddoos of same size were distributed among 400 students in which each student got 1 laddoo. If the size of each laddoos was decreased by 50 % then to how many students they distributed?
  A)
   400     done clear
  B)
                                                                    800 done clear
  C)
   1600                                                                done clear
  D)
   3200 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer19)
  Three solid cubes of type A and three solid cubes of type B are melted to form a cube. If the lengths of diagonals of cubes of type A and Type B are \[\mathbf{4}\sqrt{\mathbf{3}}\text{ }\]cm and \[\mathbf{8}\sqrt{\mathbf{3}}\text{ }\]cm respectively, then find the lateral surface area of the cube so formed.
  A)
  \[625\,c{{m}^{2}}\]                                                     done clear
  B)
   \[529\,c{{m}^{2}}\]      done clear
  C)
   \[576\,c{{m}^{2}}\]      done clear
  D)
   \[784\,c{{m}^{2}}\] done clear
  E)
   None of these done clear
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• question_answer20)
  In a right prism, the base is an equilateral triangle, Its is \[\mathbf{135}\sqrt{\mathbf{3}}\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}\] and lateral surface area is\[\mathbf{270}\,\mathbf{c}{{\mathbf{m}}^{\mathbf{2}}}\]. If height of the prism is increased by 60%, then its new volume will be ___________
  A)
   \[140\sqrt{3}\text{ c}{{\text{m}}^{3}}\]                                              done clear
  B)
   \[216\sqrt{3}\text{ c}{{\text{m}}^{3}}\]   done clear
  C)
   \[236\sqrt{3}\text{ c}{{\text{m}}^{3}}\]                                              done clear
  D)
   \[306\sqrt{3}\text{ c}{{\text{m}}^{3}}\] done clear
  E)
   None of these done clear
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• question_answer21)
  Two cubes each of volume \[\mathbf{1331}\text{ }\mathbf{c}{{\mathbf{m}}^{\mathbf{3}}}\]are joined end to end. Find the difference between total surface area and lateral surface area of the cuboid so form.
  A)
   \[576c{{m}^{2}}\]                                                      done clear
  B)
   \[484c{{m}^{2}}\]     done clear
  C)
   \[376c{{m}^{2}}\]                                                                  done clear
  D)
   \[242c{{m}^{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer22)
  0.25 cubic metre of aluminium-sheet is extended by hammering so as to cover an area of 1 hectare. The thickness of the Aluminium sheet is ____
  A)
   2.35 cm                                                            done clear
  B)
   3.25 cm      done clear
  C)
   0.0025 cm        done clear
  D)
   0.0035 cm done clear
  E)
  None of these done clear
  View Solution play_arrow

• question_answer23)
  A room is 10 m long, 6 m wide and 3 m high. It has four windows, each measuring \[\mathbf{2 m\times ~1 m}\]and a door of dimensions\[\mathbf{3}\text{ }\mathbf{m\times 1}.\mathbf{5}\text{ }\mathbf{m}\]. If the interior walls are to be coloured and a painter charges Rs. 3.25 per sq m, then the cost of colouring is Rs._________
  A)
   251.375                                                            done clear
  B)
   261.375      done clear
  C)
   271.375    done clear
  D)
   270.375 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer24)
  The difference between the areas of outside and inside surface of a cylindrical metallic pipe 14 cm long is \[\mathbf{132c}{{\mathbf{m}}^{\mathbf{2}}}\]. If the pipe is made of \[\mathbf{495c}{{\mathbf{m}}^{\mathbf{3}}}\] of metal, find the outer and inner radii of the pipe.
  A)
   4.5 cm and 3 cm           done clear
  B)
   3.5 cm and 2.0 cm done clear
  C)
   5.0 cm and 3.5 cm                                            done clear
  D)
   4.0 cm and 2.5 cm done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer25)
  The minute hand of a clock is \[\frac{\mathbf{x}}{\mathbf{2}}\] cm long. The area covered by the minute hand of the clock in 35 minutes is _________
  A)
   \[\frac{10{{x}^{2}}}{21}uni{{t}^{2}}\]                                                         done clear
  B)
   \[\frac{11{{x}^{2}}}{24}uni{{t}^{2}}\] done clear
  C)
   \[\frac{7{{x}^{2}}}{5}uni{{t}^{2}}\]                                                done clear
  D)
   \[\frac{13{{x}^{2}}}{5}uni{{t}^{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer26)
  A closed rectangular shed has dimensions \[\mathbf{28 m\times 14m}\]. It is inside a field. A cow is tied outside the shed at one of its corners with a 28 m rope. The area over which the cow can graze is ________
  A)
   \[2002{{m}^{2}}\]      done clear
  B)
                    \[1004{{m}^{2}}\] done clear
  C)
   \[728{{m}^{2}}\]                                                        done clear
  D)
   \[1992{{m}^{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer27)
  The volumes of two spheres are in the 125 : 64. If the radius is increased  by 30 % in first sphere and 50 % in second sphere, then the ratio between their surface areas is __________
  A)
  144 : 121                                               done clear
  B)
   125 : 64      done clear
  C)
   1 : 1                                                                 done clear
  D)
   169 : 144 done clear
  E)
   None of these done clear
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• question_answer28)
  A cylindrical container of radius 8 cm and height 35 cm is filled with ice-cream. The whole ice-cream is distributed among 15 children in equal cones with hemispherical tops« If the height of the conical portion is five times the radius of its base, then the radius of the ice-cream cone is _________
  A)
   3 cm                                                                done clear
  B)
   4 cm         done clear
  C)
   5 cm                                                                done clear
  D)
   6 cm done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer29)
  The difference in radii of two spheres is 2 cm and ratios of their volumes on decreasing the radius of the larger sphere by \[69\frac{3}{13}%\] and the smaller 13 sphere by \[33\frac{1}{3}%\] is 8:27. Find the difference of surface areas of two spheres.
  A)
  \[276.57c{{m}^{2}}\]  done clear
  B)
   \[168.39c{{m}^{2}}\]   done clear
  C)
  \[302.87c{{m}^{2}}\]                                                   done clear
  D)
   \[29439c{{m}^{2}}\] done clear
  E)
  None of these done clear
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• question_answer30)
  The internal and external diameters of a hallow hemispherical vessel are 22 cm and 24 cm respectively. The cost to paint 1 cm2 of the surface is Rs. 0.50. Find the total cost to paint the vessel all over.
  A)
   Rs. 669                                                             done clear
  B)
   Rs. 869        done clear
  C)
   Rs. 325                                                             done clear
  D)
   Rs. 485 done clear
  E)
   None of these done clear
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• question_answer31)
  A storage tank consists of a circular a cylinder with a hemisphere adjoined on either end. If the external diameter of the cylinder be 2.8 m and the cost of painting it on the outside at the rate of Rs. 20 per \[{{m}^{2}}\] is Rs. 765.60, then find the height of the circular cylinder.
  A)
   8.7 m                                                   done clear
  B)
   2.95 m        done clear
  C)
   435 m                                                  done clear
  D)
   5.65 m done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer32)
  If a solid sphere of radius 10 cm is melted to stretch into a wire of 1000 cm, then  curved surface area of the wire is ________
  A)
   \[7005\,c{{m}^{2}}\]                                                  done clear
  B)
   \[7266.72\,c{{m}^{2}}\] done clear
  C)
   \[3268.66c{{m}^{2}}\]                                                done clear
  D)
   \[8645.55c{{m}^{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer33)
  Water flows in a tank \[\mathbf{110 m\times 100 m}\]at the base, through a pipe whose cross-section is 2 cm by 2.5 cm at the speed of 12 km per hour. In how many hours, the water will be 6 m deep in the tank?
  A)
   70 hours                                                           done clear
  B)
   90 hours done clear
  C)
   110 hours      done clear
  D)
   130 hours done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer34)
  The diameters of the top and bottom portions of a milk can are 30 cm and 8 cm respectively. If the height of the can is 60 cm, then _________ \[\left( Use\text{ }\pi \text{ = }\frac{22}{7} \right)\]
  A)
   area of metal sheet required to make the can (without lid) is \[3692.86\,c{{m}^{2}}\] done clear
  B)
   Amount of milk which container can hold is \[18220c{{m}^{3}}\]. done clear
  C)
   area of metal sheet required = curved surface area of bottom base.       done clear
  D)
   both B and C                                             done clear
  E)
   None of these                   done clear
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• question_answer35)
  Which among the following is true about a regular tetrahedron?      
  A)
   All the faces of a regular tetrahedron are of right angled triangle.          done clear
  B)
   The lateral surface area of a regular tetrahedron is \[\frac{2\sqrt{3}}{4}{{a}^{2}}\] when 'a' is the                            done clear
  C)
   The total surface area of a regular tetrahedron = 3a2 (when 'a' is the edge) done clear
  D)
   Volume of regular tetrahedron is \[\frac{{{a}^{3}}}{3\sqrt{2}}\] done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer36)
  If in a triangle the sum of any two sides exceeds the third side by 8 cm, then its area _______
  A)
   is \[16\sqrt{3}\text{ }c{{m}^{2}}\]       done clear
  B)
   is \[10\sqrt{3}\text{ c}{{\text{m}}^{\text{2}}}\] done clear
  C)
   is \[9\sqrt{3}\text{ }c{{m}^{2}}\] done clear
  D)
   Cannot be determined done clear
  E)
   None of these done clear
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• question_answer37)
  A cylinder is within the cube touching all the vertical faces. A is the cylinder If their heights are same with the same base, then the ratio of their volumes is ___________
  A)
   21 : 33 : 11                                                       done clear
  B)
   42 : 23 : 11 done clear
  C)
   42 : 33 : 22                                                       done clear
  D)
   42 : 33 : 11 done clear
  E)
   None of these     done clear
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• question_answer38)
  A sphere is placed inside a right circular cylinder so as to touch the top, base and lateral surface of the cylinder If the radius of the sphere is 7 cm, then the volume of the cylinder is _________
  A)
   \[308c{{m}^{3}}\]                                                      done clear
  B)
   \[1156\,c{{m}^{3}}\] done clear
  C)
   \[2156\,c{{m}^{3}}\]   done clear
  D)
   \[368\,c{{m}^{3}}\] done clear
  E)
   None of these done clear
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• question_answer39)
  A square of side ?a? cm is cut from each corner of a square sheet of side 12 cm. The remaining sheet is folded to form a cuboid. If the minimum possible volume of the cuboid is M cubic cm and a is an integer, then M is _________
  A)
   20            done clear
  B)
   64          done clear
  C)
   32                                                                    done clear
  D)
   16 done clear
  E)
   None of these done clear
  View Solution play_arrow

• question_answer40)
  In a triangle, the average of any two sides is 18 cm more than half of the third side. The area of the triangle (in sq. cm) is _________
  A)
   \[162\sqrt{3}\text{ }\]                                                    done clear
  B)
   \[324\sqrt{3}\text{ }\] done clear
  C)
   \[218\sqrt{3}\text{ }\]                                        done clear
  D)
   \[420\sqrt{3}\text{ }\] done clear
  E)
  None of these done clear
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