SSC Quantitative Aptitude Mensuration Question Bank

done Mensuration-II (I) Total Questions - 51

• question_answer1)
  The radii of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is           [SSC CGL Tier II, 2017]
  A)
  27 : 20 done clear
  B)
  20 : 27 done clear
  C)
  4 : 9 done clear
  D)
  9 : 4 done clear
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• question_answer2)
  Three cubes of iron whose edges are 6 cm, 8 cm and 10 cm respectively are melted and formed into a single cube. The edge of the new cube formed is [SSC CGL Tier II, 2017]
  A)
  12 cm done clear
  B)
  14 cm done clear
  C)
  16cm done clear
  D)
  18 cm done clear
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• question_answer3)
  The radii of two concentric circles are 68 cm and 22 cm.  the area of the closed figure bounded by the boundaries of the circles is [SSC CGL Tier II, 20147]
  A)
  \[4140\,\pi \,sq\text{ }cm~\] done clear
  B)
  done clear
  C)
  \[4080\,\pi \,sq\,cm\] done clear
  D)
  \[4050\,\pi \,sq\,cm\] done clear
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• question_answer4)
  From the four corners of a rectangular sheet dimensions \[25\times 20\,cm,\] square of side \[2\,cm\]is cut off from four comers and a box is made. The volume of the box is [SSC CGL Tier II, 2017]
  A)
  \[828\text{ }c{{m}^{3}}\] done clear
  B)
  \[672\text{ }c{{m}^{3}}\] done clear
  C)
  \[500\text{ }c{{m}^{3}}\] done clear
  D)
  \[1000\,c{{m}^{3}}\] done clear
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• question_answer5)
  The radii of two solid iron spheres are 1 cm and 6 cm respectively. A hollow sphere is made by melting the two spheres. If the external radius of the hollow sphere is 9 cm, then its thickness (in cm) is [SSCCGL Tier II. 2015]
  A)
  1 done clear
  B)
  2 done clear
  C)
  0.5 done clear
  D)
  1.5 done clear
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• question_answer6)
  If a hemisphere is melted and four spheres of equal volume are made, the radius of each sphere will be equal to       [SSC CGL Tier II. 2015]
  A)
  1 /2 of the radius of the hemisphere done clear
  B)
  1/6th of the radius of the hemisphere done clear
  C)
  1/4th of the radius of the hemisphere done clear
  D)
  radius of the hemisphere done clear
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• question_answer7)
  There is a wooden sphere of radius \[6\sqrt{3}\,cm.\] The surface area of the largest possible cube cut out ' from the sphere will be [SSC CGL Tier II, 2015]
  A)
  \[864\text{ }c{{m}^{2}}\] done clear
  B)
  \[646\,\sqrt{3}\,c{{m}^{2}}\] done clear
  C)
  \[462\text{ }c{{m}^{2}}\] done clear
  D)
  \[464\sqrt{3}\,c{{m}^{2}}\] done clear
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• question_answer8)
  Base of a right pyramid is a square of side 10 cm. If the height of the pyramid is 12 cm, then its total surface area is [SSC CGL Tier n, 2015]
  A)
  \[260\text{ }c{{m}^{2}}\] done clear
  B)
  \[400\,c{{m}^{2}}\] done clear
  C)
  \[360\,c{{m}^{2}}\] done clear
  D)
  \[460\text{ }c{{m}^{2}}\] done clear
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• question_answer9)
  A right prism has a triangular base whose sides are 13 cm, 20 cm and 21 cm. If the altitude of the prism is 9 cm, then its volume is [SSC CGL Tier II, 2015]
  A)
  \[1143\,c{{m}^{3}}\] done clear
  B)
  \[1134\,c{{m}^{3}}\] done clear
  C)
  \[1413\,c{{m}^{3}}\] done clear
  D)
  \[1314\,c{{m}^{3}}\] done clear
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• question_answer10)
  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 be \[\frac{1}{27}\]th of the volume of the given cone, at what height above the base is the section made? [SSC CGL Tier II, 2014]
  A)
  19 cm done clear
  B)
  20 cm done clear
  C)
  12 cm done clear
  D)
  15 cm done clear
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• question_answer11)
  If the surface area of a sphere is \[346.5\,c{{m}^{2}},\]then its radius \[\left[ \text{taking}\,\pi =\frac{22}{7} \right]\]is [SSC CGL Tier II, 2014]
  A)
  7 cm done clear
  B)
  3.25 cm done clear
  C)
  5.25 cm done clear
  D)
  9 cm done clear
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• question_answer12)
  The height of the right pyramid whose area of the base is \[30\,{{m}^{2}}\]and volume is \[500\,{{m}^{3}},\]is [SSC CGL Tier II, 2014]
  A)
  50 m done clear
  B)
  60 m done clear
  C)
  40 m done clear
  D)
  20 m done clear
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• question_answer13)
  The base of a prism is a right angled triangle with two sides 5 cm and 12 cm. The height of the prism is 10 cm. The total surface area of the prism is [SSC CGL Tier II, 2014]
  A)
  360 sq cm done clear
  B)
  300 sq cm done clear
  C)
  330 sq cm done clear
  D)
  325 sq cm done clear
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• question_answer14)
  The base of a right prism is an equilateral triangle. If the lateral surface area and volume is \[120\,c{{m}^{2}},\] \[40\sqrt{3}\,c{{m}^{3}}\]respectively, then the side of base of the prism is [SSC CGL Tier II, 2014]
  A)
  4 cm done clear
  B)
  5 cm done clear
  C)
  7 cm done clear
  D)
  40 cm done clear
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• question_answer15)
  A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm and the thickness of wood is 2.5 cm. The volume of the wood is
  A)
  81000 cu cm done clear
  B)
  81775 cu cm done clear
  C)
  82125 cu cm done clear
  D)
  None of the above done clear
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• question_answer16)
  A rectangular water reservoir contains 42000 L   of water. If the length of reservoir is 6 m and its breadth is 3.5 m, then the depth of the reservoir is
  A)
  2 m done clear
  B)
  5 m done clear
  C)
  6 m done clear
  D)
  8 m done clear
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• question_answer17)
  A rectangular water tank is open at the top. Its capacity is \[24\,{{m}^{3}}.\]Its length and breadth are 4 m and 3 m respectively. Ignoring the thickness of the material used for building the tank, the total cost of  painting the inner and outer surfaces of the tank at Rs. 10 per \[{{m}^{2}},\]is
  A)
  Rs. 400 done clear
  B)
  Rs. 500 done clear
  C)
  Rs. 600 done clear
  D)
  Rs. 800 done clear
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• question_answer18)
  A rectangular block of metal has dimensions 21 cm 7 cm and 24 cm. The block has been melted into a sphere. The radius of the sphere  is\[\left( \text{take}\,\pi =\frac{22}{7} \right)\]
  A)
  21 cm done clear
  B)
  7 cm done clear
  C)
  14 cm done clear
  D)
  28 cm done clear
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• question_answer19)
  If each edge of a cube is increased by 50%, the percentage increase in surface area is
  A)
  125 done clear
  B)
  50   done clear
  C)
  100 done clear
  D)
  75 done clear
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• question_answer20)
  Assume that a drop of water is spherical and its diameter is one-tenth of 1 cm. A conical glass has   height equal to the diameter of its rim. If 32000  drops of water fill the glass completely, then the  eight of the glass, (in cm) is
  A)
  1 done clear
  B)
  2 done clear
  C)
  3 done clear
  D)
  4 done clear
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• question_answer21)
  The total number of spherical bullets, each of  diameter 5 cm, that can be made by utilizing the maximum of a rectangular block of lead with 11    length, 10 cm  breadth and 5 cm width is (assume that it > 3)
  A)
  equal to 8800 done clear
  B)
  less than 8800 done clear
  C)
  equal to 8400 done clear
  D)
  greater than 9000 done clear
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• question_answer22)
  If h, c, u are respectively the height, curved  surface area and volume of a right circular cone, then the value of \[3\pi v{{h}^{3}}-{{c}^{2}}{{h}^{2}}+9{{v}^{2}}\]is
  A)
  2 done clear
  B)
  \[-1\] done clear
  C)
  1 done clear
  D)
  0 done clear
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• question_answer23)
  A right circular cone is 3.6 cm high and radius of its base is 1.6 cm. It is melted and recast into a right circular cone with radius of its base as 1.2 cm. Then, the height of the cone (in cm) is
  A)
  3.6 done clear
  B)
  4.8 done clear
  C)
  6.4 done clear
  D)
  7.2 done clear
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• question_answer24)
  The diagonals of a rhombus are 12 cm and 16 cm, respectively. The length of one side is
  A)
  8 cm done clear
  B)
  6 cm done clear
  C)
  10 cm done clear
  D)
  12 cm done clear
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• question_answer25)
  The volume of a conical tent is 1232 cu m and the area of its base is 154 sq m. Find the length of the canvas required to build the tent, if the canvas is 2 m in width.\[\left( \text{take}\,\pi =\frac{22}{7} \right)\]
  A)
  270 m done clear
  B)
  272 m done clear
  C)
  276 m done clear
  D)
  275 m done clear
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• question_answer26)
  If the length of a rectangular parallelepiped is three times of its breadth and five times of its height and its volume is 14400 cu cm, then area of the total surface will be
  A)
  2420 sq cm done clear
  B)
  3320 sq cm done clear
  C)
  4320 sq cm done clear
  D)
  5320 sq cm done clear
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• question_answer27)
  The capacities of two hemispherical bowls are 6.4 L and 21.6 L, respectively. Then, the ratio of their internal curved surface areas will be 
  A)
  4 : 9 done clear
  B)
  2 : 3 done clear
  C)
  \[\sqrt{2}:\sqrt{3}\] done clear
  D)
  16 : 81 done clear
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• question_answer28)
  Let A and B be two solid spheres such that the surface area of B is300% higher than the surface area of A the volume of A is found to be k% lower than the volume of B. The value of k must be
  A)
  85.5 done clear
  B)
  92.5 done clear
  C)
  90.5 done clear
  D)
  87.5 done clear
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• question_answer29)
  The size of a wooden block is \[(15\,cm\times 12\,cm\times 20\,cm).\]How many such blocks will be required to construct a solid wooden cube of minimum size?
  A)
  45 done clear
  B)
  48 done clear
  C)
  60 done clear
  D)
  75 done clear
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• question_answer30)
  If the area of the circular shell having inner and  outer radii of 8 cm and 12 cm respectively is equal  to the total surface area of cylinder of radius \[{{R}_{1}}\] and height h, then h, in terms of \[{{R}_{1}}\] will be
  A)
  \[\frac{3R_{1}^{2}-30}{7{{R}_{1}}}\] done clear
  B)
  \[\frac{R_{1}^{2}-40}{R_{1}^{2}}\] done clear
  C)
  \[\frac{30-{{R}_{1}}}{R_{1}^{2}}\] done clear
  D)
  \[\frac{40-R_{1}^{2}}{{{R}_{1}}}\] done clear
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• question_answer31)
  From a circular sheet of paper of radius 10 cm, a sector of area 40% is removed. If the remaining part is used to make a conical surface, then the ratio of  the radius and the height of the cone is
  A)
  1 : 2 done clear
  B)
  1 : 1  done clear
  C)
  3 : 4 done clear
  D)
  4 : 3 done clear
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• question_answer32)
  A well of radius 3.5 m is dug 16 m deep. The earth removed is spread over an area of \[40\,{{m}^{2}}\]to form   platform. Height of the platform is
  A)
  1.54 m done clear
  B)
  154 m done clear
  C)
  7.7 m done clear
  D)
  77 m done clear
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• question_answer33)
  If the radius of a cylinder is decreased by 50% and the height is increased by 50% to form a new cylinder, then the volume will be decreased by
  A)
  0% done clear
  B)
  25% done clear
  C)
  62.5% done clear
  D)
  75% done clear
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• question_answer34)
  A cylinder has a diameter of 14 cm and the area of its curved surface is 220 sq cm. The volume of the cylinder is
  A)
  \[770\,c{{m}^{3}}\] done clear
  B)
  \[1000\,c{{m}^{3}}\] done clear
  C)
  \[1540\,c{{m}^{3}}\] done clear
  D)
  \[6622\,c{{m}^{3}}\] done clear
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• question_answer35)
  A well with 10 m inside diameter is dug 14 m deep. Earth taken out of it is spread all around to a width of 5 m to form an embankment. The height of the embankment is
  A)
  2.46 m done clear
  B)
  3.56 m done clear
  C)
  4.66 m done clear
  D)
  5.76 m done clear
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• question_answer36)
  The volume of a cuboid is \[1989\text{ }c{{m}^{3}},\]while its length and breadth are 17 cm and 13 cm, respectively. Find the height of the cuboid.
  A)
  9 cm done clear
  B)
  4 cm done clear
  C)
  14cm done clear
  D)
  7cm done clear
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• question_answer37)
  Three cubes of sides 1 cm, 6 cm and 8 cm are melted to form a new cube. Find half of the     surface area of the new cube.
  A)
  243 sq cm done clear
  B)
  463 sq cm done clear
  C)
      486 sq cm done clear
  D)
  293 sq cm   done clear
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• question_answer38)
                  The capacity of a cuboid tank of water is 50000 L. Find the breadth of the tank, if its length and depth are 2.5 m and 10 m respectively.
  A)
  2 m done clear
  B)
  4 m done clear
  C)
  9 m done clear
  D)
  6 m done clear
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• question_answer39)
  A solid consists of circular cylinder with exact fitting right circular cone placed on the top. The height of the cone is h. If total  volume of the solid is three times the volume of  the cone, then the height of the circular cylinder is
  A)
  \[2\,h\] done clear
  B)
  \[\frac{2\,h}{3}\] done clear
  C)
  \[4\,h\] done clear
  D)
  \[\frac{3\,h}{2}\] done clear
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• question_answer40)
  Water flows at a rate of 10 m per min from a cylindrical pipe mm in diameter. How long will it take to fill up a conical vessel whose diameter at the base is 40 cm and depth is 24 cm?
  A)
  51 min 12 s done clear
  B)
  52 min 1 s done clear
  C)
  48 min 15 s done clear
  D)
  55 min done clear
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• question_answer41)
    The heights of a cone, cylinder and hemisphere and equal if their radii are in the ratio 2 : 3 : 1, then the ratio of the their  volumes is
  A)
  2 : 9 : 2 done clear
  B)
  4 : 9 : 1 done clear
  C)
  4 : 27 : 2 done clear
  D)
  2 : 3 : 1 done clear
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• question_answer42)
  What will be the curved surface area of a right circular cylinder having length 160 cm and radius of the base is 7 cm?
  A)
  6020 sq cm done clear
  B)
  5052 sq cm done clear
  C)
  7045 sq cm done clear
  D)
  7040 sq cm done clear
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• question_answer43)
  Base of a right pyramid is a square, length of diagonal of the base is \[24\sqrt{2}\,m.\] If the volume of the pyramid is 1728 cu m its height is
  A)
  7 m done clear
  B)
  8 m done clear
  C)
  9 m done clear
  D)
  10 m done clear
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• question_answer44)
  The height of a right circular cone and the radius of its circular base are respectively 9 cm and 3 cm. The cone is cut by a plane parallel to its base so as to divide it into two parts. The volume of the frustum (i.e., the lower part) of the cone is 44 cu cm. The radius of the upper circular surface of the frustum \[(taking\,\pi =\frac{22}{7})\] is
  A)
  \[\sqrt[3]{12}\,cm\] done clear
  B)
  \[\sqrt[3]{13}\,cm\] done clear
  C)
  \[\sqrt[3]{6}\,cm\] done clear
  D)
  \[\sqrt[3]{6}\,cm\] done clear
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• question_answer45)
  The ratio of radii of two right circular cylinders is 2 : 3 and their heights are in the ratio 5:4. The ratio of their curved surface area is
  A)
  5 : 6 done clear
  B)
  3 : 4 done clear
  C)
  4 : 5 done clear
  D)
  2 : 3 done clear
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• question_answer46)
  The frustum of a right circular cone has the diameters of base 10 cm, of top 6 cm and a height of 5 cm. Find its slant height.
  A)
  \[\sqrt{29}\,cm\] done clear
  B)
  \[3\sqrt{3}\,cm\] done clear
  C)
  \[\sqrt{13}\,cm\] done clear
  D)
  \[\sqrt{13}\,cm\] done clear
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• question_answer47)
  A cone of radius r cm and height h cm is divided into two parts by drawing a plane through the middle point of its height and parallel to the base. What is the ratio of the volume of the original cone to the volume of the smaller cone?
  A)
  4 : 1 done clear
  B)
  8 : 1 done clear
  C)
  2 : 1 done clear
  D)
  6 : 1 done clear
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• question_answer48)
  A conical cap has the base diameter 24 cm and height 16 cm. What is the cost of painting the surface of the cap at the rate of 70 paise per sq cm?
  A)
  Rs. 520 done clear
  B)
  Rs. 524 done clear
  C)
  Rs. 528 done clear
  D)
  Rs. 532 done clear
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• question_answer49)
  Find the number of lead balls of diameter 2 cm each, that can be made from a sphere of diameter 16 cm.
  A)
  512 done clear
  B)
  2055 done clear
  C)
  2058     done clear
  D)
  2085 done clear
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• question_answer50)
  How many spherical bullets can be made out of a solid cube whose edge measures 44 cm, each bullet being 4 cm in diameter?
  A)
  2550 done clear
  B)
  2541 done clear
  C)
  2500     done clear
  D)
  2575 done clear
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• question_answer51)
  A conical flask is full of water. The flask has base radius r and height h. This water is poured into a cylindrical flask of base radius mr. The height of water in the cylindrical flask is
  A)
  \[\frac{h}{2}{{m}^{2}}\] done clear
  B)
  \[\frac{2h}{m}\] done clear
  C)
  \[\frac{h}{3{{m}^{2}}}\] done clear
  D)
  \[\frac{m}{2h}\] done clear
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