10th Class Mathematics Surface Areas and Volumes Question Bank

done Surface Area and Volume Total Questions - 49

• question_answer1)
  A cuboidal metal of dimensions \[\text{44 cm}\times \text{3}0\text{ cm}\] \[\times \text{15 cm}\] was melted and cast into a cylinder of height 28 cm. Find its radius.
  A)
   20cm                                    done clear
  B)
   15cm done clear
  C)
   10cm                    done clear
  D)
          18cm done clear
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• question_answer2)
  The length of the longest rod which can, be kept inside a rectangular box is 27 cm. If the length and the breadth of the box are 23 cm and 10 cm respectively, find its height.
  A)
   8cm                                       done clear
  B)
   10cm done clear
  C)
   12cm                    done clear
  D)
          14cm done clear
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• question_answer3)
  The volume of a cube is numerically equal to its surface area. What is the length of its side?                                 
  A)
   6 units                                  done clear
  B)
   8 units done clear
  C)
   9 units                  done clear
  D)
          10 units done clear
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• question_answer4)
  The total surface area of a cylinder is 220 sq cm with height 6.5 cm. Find its volume.
  A)
   \[\text{25}.0\text{25 c}{{\text{m}}^{\text{3}}}\]              done clear
  B)
   \[\text{2}.\text{5}0\text{25 c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{25}0\text{2}.\text{5 c}{{\text{m}}^{\text{3}}}\]    done clear
  D)
          \[\text{25}0.\text{25 c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer5)
  The lateral surface area of a cylinder is 176 \[\text{c}{{\text{m}}^{\text{2}}}\]and its base area is\[~\text{38}.\text{5}\,\text{c}{{\text{m}}^{\text{2}}}\].What is its volume?
  A)
   \[\text{83}0\text{ c}{{\text{m}}^{\text{3}}}\]                                    done clear
  B)
   \[\text{38}0\text{ c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{3}0\text{8 c}{{\text{m}}^{\text{3}}}\]                                    done clear
  D)
   \[\text{8}0\text{3 c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer6)
  Identify the ratio of lateral surface areas of two cylinders with equal heights.
  A)
   H: h                                       done clear
  B)
   R: r done clear
  C)
   1: 2                        done clear
  D)
          2:3 done clear
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• question_answer7)
  A cone and a hemisphere have equal bases and equal volumes. Identify the ratio of their heights.
  A)
   1 : 3                       done clear
  B)
          1 : 2 done clear
  C)
   2 : 1                                       done clear
  D)
   3 : 1 done clear
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• question_answer8)
  The area of the base of a cone is 616 sq cm. Its height is 48 cm. Find its total surface area.
  A)
   \[\text{2816}\,\text{c}{{\text{m}}^{\text{2}}}\]               done clear
  B)
          \[\text{2861 c}{{\text{m}}^{\text{2}}}\] done clear
  C)
   \[\text{2618}\,\text{c}{{\text{m}}^{\text{2}}}\]               done clear
  D)
          \[\text{2681 c}{{\text{m}}^{\text{2}}}\] done clear
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• question_answer9)
  From a circle of radius 15 cm, a sector central angle\[~\text{216}{}^\circ \]is cut and its bounding radii are joined without overlap so as to form a cone. Find its volume.
  A)
   \[\text{1}0\text{81}.\text{3}\,\text{c}{{\text{m}}^{\text{3}}}\]    done clear
  B)
          \[\text{1}0\text{71}.\text{3}\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{1}0\text{18}.\text{3}\,\text{c}{{\text{m}}^{\text{3}}}\]    done clear
  D)
          \[~\text{1}0\text{61}.\text{9}\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer10)
  A cylindrical vessel of diameter 9 cm has some water in it. A cylindrical iron piece of diameter 6 cm and height 4.5 cm is dropped in it. After it was completely immersed, what is the rise in the level of water?
  A)
   0.8 cm                                  done clear
  B)
   0.5 cm done clear
  C)
   0.1 cm                  done clear
  D)
          0.3 cm done clear
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• question_answer11)
  The diameter of a copper sphere is 6 cm. It is beaten and drawn into a wire of diameter 0.2 cm. What is the length of the wire?
  A)
   36 cm       done clear
  B)
                          360 cm done clear
  C)
   3600 cm               done clear
  D)
          306 cm done clear
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• question_answer12)
  A cylindrical vessel of diameter 4 cm is partly filled with water. 300 lead balls are dropped in it. The raise in water level is 0.8 cm. Find the diameter of each ball.
  A)
   0.8 cm                                  done clear
  B)
   0.4 cm done clear
  C)
   0.2 cm                  done clear
  D)
          0.6 cm done clear
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• question_answer13)
  Three solid glass balls of radii 'r' cm, 6 cm and 8 cm are melted into a solid sphere of radius 9 cm. Find the value of 'r'.
  A)
   \[\frac{1}{4}cm\]                             done clear
  B)
   \[\frac{1}{3}cm\] done clear
  C)
   \[\frac{1}{2}cm\]             done clear
  D)
          1 cm done clear
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• question_answer14)
  A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. What is the volume of steel used?
  A)
   \[\text{42}.\text{15 c}{{\text{m}}^{\text{3}}}\]                done clear
  B)
   \[~\text{41}.\text{52 c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{41}.\text{25}\,\text{c}{{\text{m}}^{\text{3}}}\]      done clear
  D)
          \[\text{43}.\text{21c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer15)
  A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. Find the height of the cone.
  A)
   14cm                    done clear
  B)
          12cm done clear
  C)
   16cm                    done clear
  D)
          18cm done clear
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• question_answer16)
  A circus tent is in the form of a cone over a cylinder. The diameter of the base is 9 m, the height of cylindrical part is 4.8 m and the total height of the tent is 10.8m. What area of canvas is required for the tent?
  A)
   24.184 sq. m    done clear
  B)
          2418.4 sq. m done clear
  C)
   241.84sq.m    done clear
  D)
          24.164 sq. m done clear
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• question_answer17)
  If the radii of the circular ends of a conical bucket of height 45 cm are 28 cm and 7 cm, what is the capacity of the bucket?
  A)
   \[\text{4815}0\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
  B)
                          \[\text{4851}0\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{48105}\,\text{c}{{\text{m}}^{\text{3}}}\]             done clear
  D)
          \[\text{48}0\text{15}\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer18)
  The height of a cone is 30 cm. A small cone is cut off at the top by a plane parallel to the base. If its volume is\[\frac{1}{27}\]. the volume of cone, what is the height at which the section is made?
  A)
   10 cm done clear
  B)
                          15 cm done clear
  C)
   20 cm   done clear
  D)
          19 cm done clear
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• question_answer19)
  A top is of the shape of a cone over a hemisphere. The radius of the hemisphere is 3.5 cm. The total height of the top is 15.5 cm. Find the total area of the top.
  A)
   \[\text{214}.\text{5}\,\text{c}{{\text{m}}^{\text{2}}}\]     done clear
  B)
          \[\text{21}.\text{45}\,\text{c}{{\text{m}}^{\text{2}}}\] done clear
  C)
   \[~\text{215}.\text{4}\,\text{c}{{\text{m}}^{\text{2}}}\]     done clear
  D)
          \[\text{21}.\text{43}\,\text{c}{{\text{m}}^{\text{2}}}\] done clear
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• question_answer20)
  The base radius of a cylinder is\[1\frac{2}{3}\]. times its height. The cost of painting its curved surface area at \[\text{2 paise}/\text{c}{{\text{m}}^{\text{2}}}\]is ` 92.40. Find the volume of the liquid.
  A)
   \[\text{8}0\text{85}0\text{ c}{{\text{m}}^{\text{3}}}\]                  done clear
  B)
   \[\text{8}0\text{58}0\text{ c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{8}0\text{5}0\text{8 c}{{\text{m}}^{\text{3}}}\]    done clear
  D)
          \[\text{8}00\text{5}0\text{8 c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer21)
  A cylindrical vessel contains 49.896 litres of liquid. The cost of painting its curved surface area at 2 paise/sq cm is ` 95.04. Find its total surface area.
  A)
   \[\text{5724 c}{{\text{m}}^{\text{2}}}\]               done clear
  B)
          \[~\text{7524 c}{{\text{m}}^{\text{2}}}\] done clear
  C)
   \[\text{5742 c}{{\text{m}}^{\text{2}}}\]               done clear
  D)
          \[\text{7254 c}{{\text{m}}^{\text{2}}}\] done clear
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• question_answer22)
  The ratio of base radius and height of a cone is 3 :4. If the cost of smoothening the curved surface area at 5 paise/sq cm is ` 115.50, find the volume of cone.
  A)
   \[\text{12963}\,\text{c}{{\text{m}}^{\text{3}}}\]                             done clear
  B)
   \[\text{12693}\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{12936}\,\text{c}{{\text{m}}^{\text{3}}}\]             done clear
  D)
          \[\text{12639}\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer23)
  A vessel is conical in shape. If its volume is 33.264 litres and height is 72 cm, find the cost of repairing its curved surface area at? 12/sq m.
  A)
   ` 5.94                   done clear
  B)
   ` 6.94 done clear
  C)
   ` 7.95   done clear
  D)
          ` 9.65 done clear
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• question_answer24)
  The cost of painting the curved surface area of a cone at \[\text{5 ps}/\text{c}{{\text{m}}^{\text{2}}}\]is ` 35.20, find the volume of the cone if its slant height is 25 cm.
  A)
   \[\text{1223}\,\text{c}{{\text{m}}^{\text{3}}}\]               done clear
  B)
          \[\text{1232}\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[~\text{1323}\,\text{c}{{\text{m}}^{\text{3}}}\]             done clear
  D)
          \[\text{1332}\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer25)
  A piece of metal pipe is 77 cm long with inside diameter of the cross section as 4 cm. If the outer diameter is 4.5 cm and the metal weighs 8 gm/cu cm, find the weight of pipe.
  A)
   2.057 kg                               done clear
  B)
   20.57 kg done clear
  C)
   205.7 kg               done clear
  D)
          2.097 kg done clear
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• question_answer26)
  A rectangular solid metallic cuboid \[\text{9 cm}\times \text{8 cm }\times \text{2 cm}\] is melted and recast into solid cubes each of side 2 cm. How many such solid cubes can be made?
  A)
   20                                          done clear
  B)
   18   done clear
  C)
   12                          done clear
  D)
          15 done clear
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• question_answer27)
  The side of a solid metallic cube is 50 cm. It is melted and recast into 8000 similar solid cubical dice. Find the side of each die.
  A)
   2.5 cm                                  done clear
  B)
   6 cm done clear
  C)
   1.9cm                   done clear
  D)
          5.2cm done clear
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• question_answer28)
  Water flows at the rate of 5 km per hour through a pipe of diameter 14 cm into a rectangular tank which is 25 m long and 22 m wide. Find the time in which the level of water in the tank rises by 21 cm. [Take\[\pi =\frac{22}{7}\].]
  A)
   2 hours                                done clear
  B)
   5 hours done clear
  C)
   3 hours                done clear
  D)
          1.5 hours done clear
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• question_answer29)
  Two right circular cones X and Y are made such that X has a radius three times the radius of Y and Y has a volume half the volume of X. What is the ratio of heights of X and Y?
  A)
   5:8                                         done clear
  B)
   4:7 done clear
  C)
   2:9                         done clear
  D)
          3:5 done clear
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• question_answer30)
  Rain water from a roof \[\text{22 m }\times \text{ 2}0\text{ m}\] drains into a cylindrical vessel with diameter of base 2 m and height 3.5 m. If the vessel is just full, find the amount of rainfall in cm.
  A)
   4.5 cm  done clear
  B)
          2.5 cm done clear
  C)
   3 cm      done clear
  D)
          1 cm done clear
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• question_answer31)
  The diameter of a solid metallic sphere is 16 cm. The sphere is melted and recast into 8 similar solid spherical balls. What is the radius of the each of the balls?
  A)
   2 cm                                      done clear
  B)
   3 cm done clear
  C)
   4 cm                      done clear
  D)
          6 cm done clear
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• question_answer32)
  A hemispherical bowl of internal diameter 36 cm is full of liquid. The liquid is to be filled into cylindrical shaped bottles each of radius 3 cm and height 9 cm. How many bottles are required to empty the bowl?
  A)
   24                                          done clear
  B)
   35   done clear
  C)
   12                          done clear
  D)
          48 done clear
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• question_answer33)
  If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.
  A)
   1 :4                        done clear
  B)
          2:3 done clear
  C)
   1:2                         done clear
  D)
          5:7 done clear
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• question_answer34)
  56 circular plates, each of radius 5 cm and thickness 0.25 cm, are placed one above the other to form a solid right circular cylinder. Find the volume of the cylinder so formed.
  A)
   \[\text{9}00\text{ c}{{\text{m}}^{\text{3}}}\]                    done clear
  B)
          \[\text{885 c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[~\text{11}00\text{ c}{{\text{m}}^{\text{3}}}\]               done clear
  D)
          \[~\text{125}0\,\text{c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer35)
  A semicircular piece of paper of radius 14 cm is rolled to form a cone of the largest possible size. Find the capacity of the cone.
  A)
   \[\text{721}.\text{5c}{{\text{m}}^{\text{3}}}\]                 done clear
  B)
          \[\text{645}.\text{1}0\text{c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{449}.\text{64 c}{{\text{m}}^{\text{3}}}\]    done clear
  D)
          \[\text{622}.\text{37 c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer36)
  In a solid cylinder of height 10 cm and diameter 8 cm, two equal conical cavities have been made at both its ends. If the diameter of the cavity is 6 cm and height 4 cm, find the volume of the remaining solid in terms of\[\pi \].
  A)
   \[\text{95}\,\pi \text{ c}{{\text{m}}^{\text{3}}}\]      done clear
  B)
          \[\text{136}\,\pi \text{ c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{216}\,\pi \text{ c}{{\text{m}}^{\text{3}}}\]     done clear
  D)
         \[\text{192}\,\,\pi \text{ c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer37)
  A solid sphere and a solid hemisphere have the same total surface area. Find the ratio of their volumes.
  A)
   \[\sqrt{3}:1\]                    done clear
  B)
   \[3\sqrt{3}:5\] done clear
  C)
   \[3\sqrt{3}:4\]  done clear
  D)
          \[1:\sqrt{3}\] done clear
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• question_answer38)
  A sphere, of diameter 12 cm, is dropped into a right circular cylindrical vessel, partly filled with water. If the sphere is completely immersed in water, the water level in the cylindrical vessel rises by\[3\frac{5}{9}\]cm. Find the diameter of the cylindrical vessel.
  A)
   16cm                    done clear
  B)
          18cm done clear
  C)
   12cm                    done clear
  D)
          13cm done clear
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• question_answer39)
  The largest right circular cone is carved out of a cube whose edge is of length 'p' units. Find the volume of the cone.
  A)
   \[\frac{\pi {{p}^{3}}}{12}cu.units\]          done clear
  B)
   \[\frac{\pi {{p}^{3}}}{4}cu.units\] done clear
  C)
   \[\pi {{p}^{3}}cu.units\]               done clear
  D)
          \[\frac{\pi {{p}^{3}}}{5}cu.units\] done clear
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• question_answer40)
  A right-angled triangle ABC, where\[\angle B={{90}^{o}}\], is rotated about BC. If BC = 16 cm and AC = 20 cm, find the volume of the right circular cone traced out by the triangle.
  A)
   \[\text{2413}\,\text{c}{{\text{m}}^{\text{3}}}\]               done clear
  B)
          \[\text{2311 c}{{\text{m}}^{\text{3}}}\] done clear
  C)
   \[\text{1254}\,\text{c}{{\text{m}}^{\text{3}}}\]               done clear
  D)
          \[\text{1725c}{{\text{m}}^{\text{3}}}\] done clear
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• question_answer41)
  A bucket of height 16 cm made up of metal sheet is in the form of frustum of a right circular cone with radii of its lower and upper ends as 3 cm and 15 cm respectively. What is the slant height of the bucket?
  A)
   15cm                                    done clear
  B)
   20cm done clear
  C)
   5cm                       done clear
  D)
          12cm done clear
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• question_answer42)
  A right-angled triangular plate of smaller sides measuring 5 cm and 12 cm is rotated about the longest side to trace a double cone as shown in the figure. Find the ratio of the curved surface areas of the two cones.
  A)
   6:1                         done clear
  B)
          5:12 done clear
  C)
   3:14                       done clear
  D)
          6:5 done clear
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• question_answer43)
  The largest possible cube is made from a wooden sphere of radius \[6\sqrt{3}\,cm\]cm. Find the surface area of the cube.
  A)
   \[\text{864}\,\text{c}{{\text{m}}^{\text{2}}}\]                                  done clear
  B)
   \[\text{542}\,\text{c}{{\text{m}}^{\text{2}}}\] done clear
  C)
   \[\text{735}\,\text{c}{{\text{m}}^{\text{2}}}\]                  done clear
  D)
          \[\text{625}\,\text{c}{{\text{m}}^{\text{2}}}\] done clear
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• question_answer44)
  The radii of circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area.
  A)
   \[\text{1564}.\text{15}\,\text{c}{{\text{m}}^{\text{2}}}\]            done clear
  B)
   \[\text{7599}.\text{43}\,\text{c}{{\text{m}}^{\text{2}}}\] done clear
  C)
   \[\text{6542}.\text{1 c}{{\text{m}}^{\text{2}}}\]    done clear
  D)
          \[\text{8265}.\text{14}\,\text{c}{{\text{m}}^{\text{2}}}\] done clear
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• question_answer45)
  The ratio of the radii of two spheres is 3 :2. Find the ratio of their volumes.
  A)
   25:4                                       done clear
  B)
   5:16 done clear
  C)
   9:14                       done clear
  D)
          27:8 done clear
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• question_answer46)
  A cylindrical can whose base is horizontal and of internal radius 3.5 cm contains sufficient water so that when a solid sphere is placed in the can, water just covers the sphere. Given that the sphere just fits in the can, find the depth of water in the can before the sphere was put into it.
  A)
   2.3 cm                                  done clear
  B)
   5.1 cm done clear
  C)
   1.5cm                                   done clear
  D)
   3.2cm done clear
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• question_answer47)
  The internal and external radii of a hemispherical metallic vessel are 7 cm and 10.5 cm respectively. If \[\text{1 c}{{\text{m}}^{\text{3}}}\]of the metal weighs 10 g, find the weight of the vessel.
  A)
   25.15kg                done clear
  B)
          32.1 kg done clear
  C)
   17.07kg                done clear
  D)
          16.27kg done clear
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• question_answer48)
  A tent is made in the form of a frustrum A of a right circular cone surmounted by another right circular cone B. The diameter of the ends of the frustrum A are 8 m and 4 m, its height is 3 m and the height of the cone B is 2 m. What is the area of the canvas required for the tent?
  A)
   \[\text{86}.\text{75 }{{\text{m}}^{\text{2}}}\]                  done clear
  B)
   \[\text{85}.\text{77 }{{\text{m}}^{\text{2}}}\] done clear
  C)
   \[\text{86}.\text{77 }{{\text{m}}^{\text{2}}}\]                  done clear
  D)
          \[\text{87}.\text{67 }{{\text{m}}^{\text{2}}}\] done clear
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• question_answer49)
  What is the maximum distance between any two points of a cube of side T units?
  A)
   \[(\sqrt{2}+1)l\,units\] done clear
  B)
   \[\sqrt{2}\,l\,units\] done clear
  C)
    \[\sqrt{3}\,l\,units\]      done clear
  D)
          \[2\,l\,units\] done clear
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