8th Class Mental Ability Cubes and Cube Roots Question Bank

done Cubes and Cube_Roots Total Questions - 40

• question_answer1)
  Find the value of \[\sqrt[3]{0.512}.\]
  A)
   0.12                                       done clear
  B)
   0.5         done clear
  C)
          8.0         done clear
  D)
          0.8                         done clear
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• question_answer2)
  Find the cube root of \[2\frac{93}{125}.\]
  A)
   \[\frac{3}{5}\]                   done clear
  B)
          \[\frac{9}{5}\]                   done clear
  C)
                   \[\frac{7}{5}\]                   done clear
  D)
          \[\frac{2}{5}\]                                   done clear
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• question_answer3)
  Identify the simplest form of the expression \[\sqrt[3]{27\times {{x}^{3}}{{y}^{9}}}.\]
  A)
   \[3\,x{{y}^{3}}\]                              done clear
  B)
  \[3\,x{{y}^{3}}\]               done clear
  C)
          \[\frac{2}{7}\]                   done clear
  D)
          \[\frac{4}{7}\] done clear
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• question_answer4)
  Identify the value of\[\sqrt[3]{\frac{0.064\times 125}{343}}\].
  A)
   \[\frac{1}{7}\]                                   done clear
  B)
   \[\frac{2}{7}\]                   done clear
  C)
          \[\frac{3}{7}\]                   done clear
  D)
          \[\frac{4}{7}\]                   done clear
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• question_answer5)
  If \[x=76\]and \[y=49,\]find the value of \[\sqrt[3]{(x-y)(x+y)}.\]             
  A)
   51                          done clear
  B)
          15          done clear
  C)
   3                             done clear
  D)
          25                                          done clear
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• question_answer6)
  The volume of a sphere is given by \[\frac{4}{3}\pi {{r}^{3}}.\] Find the radius of a sphere whose volume is \[1047.816\text{ }c{{m}^{3}}.\] (Take n to be\[\frac{22}{7}.\])
  A)
   5.3 cm                                  done clear
  B)
   7.3 cm                  done clear
  C)
          6.3 cm done clear
  D)
          8.3 cm                  done clear
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• question_answer7)
  The volume of material used to make a cube is \[1728\text{ }c{{m}^{3}}.\]What is the length of its side?
  A)
   17 cm                                   done clear
  B)
   18 cm   done clear
  C)
                                          14 cm   done clear
  D)
          12 cm done clear
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• question_answer8)
  The volume of water in a measuring cylinder is \[200\text{ }c{{m}^{3}}.\]When a cube is immersed in the water, the cylinder reads\[543\,c{{m}^{3}}.\] Find the volume of the cube.
  A)
  \[279\text{ }c{{m}^{3}}\]                              done clear
  B)
  \[363\text{ }c{{m}^{3}}\]              done clear
  C)
         \[343\text{ }c{{m}^{3}}\]              done clear
  D)
         \[~329\text{ }c{{m}^{3}}\]                           done clear
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• question_answer9)
  Find the value of\[{{1}^{3}}+{{2}^{3}}+{{3}^{3}}+{{4}^{3}}.\]
  A)
  \[{{(1+2+3+4)}^{3}}\] done clear
  B)
         \[{{(1+2+3+4)}^{2}}\] done clear
  C)
         \[{{(2+2+2+2)}^{2}}\] done clear
  D)
         \[{{(1\times 2\times 3\times 4)}^{2}}\] done clear
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• question_answer10)
  Find the cube root of 1000000.
  A)
  \[10\times 0.1\]                done clear
  B)
         \[0.1\times 0.1\]              done clear
  C)
         \[10\times 10\]                 done clear
  D)
         \[100\times 10\]                               done clear
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• question_answer11)
  Find the smallest number by which 1125 must be multiplied to get a perfect cube.
  A)
   5             done clear
  B)
          7             done clear
  C)
          9             done clear
  D)
          3                                             done clear
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• question_answer12)
  Find the largest four digit number which is a perfect cube.
  A)
   9999                      done clear
  B)
          1000     done clear
  C)
   9261      done clear
  D)
   8000                      done clear
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• question_answer13)
  Find the cube root of  \[\frac{32768}{512}\]                               
  A)
   16          done clear
  B)
          12          done clear
  C)
          8                               done clear
  D)
          4                             done clear
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• question_answer14)
  Find the least possible value of B for which \[6561\times B\]is a perfect cube.
  A)
   1             done clear
  B)
          2             done clear
  C)
   3             done clear
  D)
          4                                             done clear
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• question_answer15)
  Find the units digit in the cube of 63.
  A)
   9             done clear
  B)
          3             done clear
  C)
          7                             done clear
  D)
          6                             done clear
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• question_answer16)
  If \[\frac{\sqrt[3]{0.729}}{k}=\sqrt[3]{1000000},\] find the value of k.
  A)
   0.0009                  done clear
  B)
          9000     done clear
  C)
   900        done clear
  D)
          0.009                    done clear
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• question_answer17)
  Find the prime factorization form of the cube root of\[{{3}^{12}}\times {{5}^{9}}.\]
  A)
  \[{{3}^{4}}\times {{5}^{9}}\]        done clear
  B)
         \[{{3}^{6}}\times {{5}^{3}}\]        done clear
  C)
  \[{{3}^{3}}\times {{5}^{3}}\]        done clear
  D)
         \[{{3}^{4}}\times {{5}^{3}}\]                        done clear
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• question_answer18)
  What is the smallest number by which 3600 must be divided to make it a perfect cube?
  A)
   450        done clear
  B)
          500        done clear
  C)
          400        done clear
  D)
          100                        done clear
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• question_answer19)
  Identify the cube root of the number obtained by finding the L.C.M. of 24 and 108.
  A)
   8             done clear
  B)
          7             done clear
  C)
          6             done clear
  D)
          9 done clear
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• question_answer20)
  Find the value of \[\sqrt[3]{\sqrt{0.000064}}.\]
  A)
   \[\frac{4}{10}\]                done clear
  B)
   \[\frac{2}{10}\]                done clear
  C)
   \[\frac{6}{10}\]                done clear
  D)
          \[\frac{8}{10}\]                done clear
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• question_answer21)
  If \[{{8}^{n+1}}=512,\]find the value of \[\sqrt[3]{n+998}.\]
  A)
   8             done clear
  B)
          4       done clear
  C)
   10          done clear
  D)
          12                          done clear
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• question_answer22)
  If the cube root of 132651 is 51, find the value of the given expression.

  \[\sqrt[3]{132.651}+\sqrt[3]{0.132651}+\sqrt[3]{0.000132651}\]

  A)
   5.661                    done clear
  B)
          56.61    done clear
  C)
   566.1    done clear
  D)
          5661                      done clear
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• question_answer23)
  Find the value of\[\sqrt[3]{375\times 243}.\]
  A)
   55          done clear
  B)
          45          done clear
  C)
          35          done clear
  D)
          65                          done clear
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• question_answer24)
  Small cubes of edge 2 cm are to be packed in a rectangular container measuring 6 cm by 5 cm and 4 cm. How many cubes can be packed in the container?
  A)
   17         done clear
  B)
          18          done clear
  C)
   16          done clear
  D)
          15 done clear
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• question_answer25)
  What is the capacity of a container whose shape is a cube of side 20cm?
  A)
  \[2000\text{ }c{{m}^{3}}\]            done clear
  B)
         \[~4000\text{ }c{{m}^{3}}\]         done clear
  C)
         \[~6000\text{ }c{{m}^{3}}\]         done clear
  D)
         \[~8000\text{ }c{{m}^{3}}\] done clear
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• question_answer26)
  A box measures 1 m by 1 m by 1 m. What are its measures in cm?
  A)
  \[10\text{ }cm\text{ }\times \text{ }10\text{ }cm\text{ }\times \text{ }10\text{ }cm\] done clear
  B)
     \[~100\text{ }cm\text{ }\times \text{ }100\text{ }cm\text{ }\times \text{  }100\text{ }cm\] done clear
  C)
  \[~40\text{ }cm\text{ }\times \text{ }40\text{ }cm\text{ }\times \text{ }40\text{ }cm\] done clear
  D)
     \[50\text{ }cm\text{ }\times \text{ }56\text{ }cm\text{ }\times \text{ }50\text{ }cm\] done clear
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• question_answer27)
  A shopkeeper bought rubbers in boxes of 10 cm by 10 cm by 10 cm. He packed the boxes in a carton measuring 0.8 m by 0.6 m by 0.4 m. How many boxes can be packed in the carton?
  A)
   194                        done clear
  B)
          164                        done clear
  C)
   192                        done clear
  D)
          184                        done clear
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• question_answer28)
  Find the wrong number in the given series.

  2, 9, 28, 65, 126, 216, 344

  A)
   126                        done clear
  B)
          28          done clear
  C)
          216        done clear
  D)
          65                          done clear
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• question_answer29)
  Find the smallest number by which 5324 must be divided to get a perfect cube.
  A)
   4             done clear
  B)
          3             done clear
  C)
   2                             done clear
  D)
          1 done clear
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• question_answer30)
  Which of the following are perfect cubes? (i) 10000                               (ii) 4913 (iii) 6589                               (iv) 3528
  A)
   Only (ii) and (iii)         done clear
  B)
   Only (iii) and (iv) done clear
  C)
          Only (i) and (iv)   done clear
  D)
           Only (ii) and (iv) done clear
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• question_answer31)
  Find the cube root of\[\left( \frac{1}{8}\times \frac{125}{64} \right)\]
  A)
   \[\frac{5}{8}\]                   done clear
  B)
          \[\frac{372}{512}\]         done clear
  C)
          \[2\frac{1}{2}\]                 done clear
  D)
          \[15\frac{5}{8}\] done clear
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• question_answer32)
  Which of the following are true?

  (i) The cube of any odd number is even. (ii) A perfect cube does not end with two zeros. (iii) There is no perfect cube which ends with 8. (iv) The cube of a single digit number may be a single digit number.

  A)
   Only (ii) and (iii)  done clear
  B)
            Only (i) and (ii) done clear
  C)
   Only (i) and (iii)    done clear
  D)
           Only (ii) and (iv) done clear
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• question_answer33)
  Find the cube root of 79507.
  A)
   37         done clear
  B)
          53          done clear
  C)
          43          done clear
  D)
          57                                          done clear
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• question_answer34)
  Identify the value of \[{{(0.03)}^{3}}.\]
  A)
   0.000270             done clear
  B)
          0.000027             done clear
  C)
   0.000072             done clear
  D)
          0.000030 done clear
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• question_answer35)
  Find the volume of a cube of side 13 cm.
  A)
  \[2197\text{ }c{{m}^{3}}\]            done clear
  B)
         \[~2179\text{ }c{{m}^{3}}\]         done clear
  C)
         \[2719\text{ }c{{m}^{3}}\]            done clear
  D)
         \[~2917\text{ }c{{m}^{3}}\]                         done clear
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• question_answer36)
  Identify the value of \[({{7}^{3}}-{{6}^{3}}).\]
  A)
   112                        done clear
  B)
          162        done clear
  C)
          127        done clear
  D)
          189                        done clear
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• question_answer37)
  A cubic water tank has sides of length 2.143 m. What is the capacity of the tank in litres?
  A)
   9.8416                  done clear
  B)
          9.6456                  done clear
  C)
   9.8926                                  done clear
  D)
   9.7426                  done clear
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• question_answer38)
  Which of the following are equal?

  21 + 23 + 25 + 27 + 29 13 + 15 + 17 + 19 31 + 37 + 41 + 43 \[5\times 5\times 5\]

  A)
   Only (i) and (ii)           done clear
  B)
   Only (ii) and (iii) done clear
  C)
          Only (i) and (iii)   done clear
  D)
           Only (i) and (iv) done clear
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• question_answer39)
  Find the cube root of \[{{a}^{6}}{{b}^{3}}.\]
  A)
   \[ab\]                   done clear
  B)
          \[{{a}^{3}}{{b}^{2}}\]     done clear
  C)
          \[{{a}^{2}}b\]                    done clear
  D)
          \[{{a}^{2}}{{b}^{2}}\]                     done clear
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• question_answer40)
  Which is the only cube having the same value as its cube root?
  A)
   10          done clear
  B)
          0.1         done clear
  C)
          11          done clear
  D)
          1.0 done clear
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