8th Class Mathematics Cubes and Cube Roots Question Bank

done Cubes and Cube Roots Total Questions - 25

• question_answer1)
  The value of \[{{45}^{3}}-{{65}^{3}}-{{20}^{3}}\]is __.
  A)
   175500                       done clear
  B)
   -191500          done clear
  C)
   170000           done clear
  D)
          -170000          done clear
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• question_answer2)
  If \[\sqrt[3]{-2744}\div \sqrt[3]{0.008}=x\],then the value of x is __.
  A)
   70                   done clear
  B)
          -70      done clear
  C)
   14                   done clear
  D)
          -14                  done clear
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• question_answer3)
  If \[\sqrt[3]{3\left( \sqrt[3]{x}-\frac{1}{\sqrt[3]{x}} \right)}=2\], then \[\sqrt[3]{x}+\frac{1}{\sqrt[3]{x}}=\_\_\_\_\_\].
  A)
   \[\frac{10}{3}\]                      done clear
  B)
         \[-\frac{10}{3}\]         done clear
  C)
   \[\frac{3}{15}\]                      done clear
  D)
          Both [a] and [b] done clear
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• question_answer4)
  How many cubes of side 2 cm can be packed in a cubical box with inner side equal to 4 cm?
  A)
   6                                 done clear
  B)
   4                     done clear
  C)
   8                     done clear
  D)
          2                     done clear
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• question_answer5)
  Find the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube.
  A)
   4                                 done clear
  B)
   2         done clear
  C)
   6                     done clear
  D)
          8 done clear
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• question_answer6)
  In the five digit number 1b6a3, a is the greatest single digit perfect cube and twice of it exceeds b by 7. Then the sum of the number and its cube root is __.
  A)
   18700             done clear
  B)
   11862 done clear
  C)
          19710 done clear
  D)
          25320 done clear
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• question_answer7)
  The value of \[\sqrt[3]{\frac{{{a}^{6}}\times {{b}^{3}}\times {{c}^{21}}}{{{c}^{9}}\times {{a}^{12}}}}\] is ______.
  A)
   \[\frac{-b{{c}^{3}}}{{{a}^{2}}}\]                     done clear
  B)
   \[\frac{b{{c}^{4}}}{{{a}^{2}}}\]          done clear
  C)
   \[\frac{-a{{b}^{4}}}{{{c}^{2}}}\]         done clear
  D)
          \[\frac{-b{{c}^{4}}}{{{a}^{2}}}\] done clear
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• question_answer8)
  Three numbers are in the ratio 2 : 3 : 5 to one another. The sum of their cubes is 54880. The numbers are____.
  A)
   14, 21, 35                   done clear
  B)
          12, 15, 17       done clear
  C)
          14, 18, 21                   done clear
  D)
          21, 28, 32 done clear
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• question_answer9)
  The cube of a 2-digit number will contain
  A)
   4 digits                        done clear
  B)
          5 digits                        done clear
  C)
          6 digits                        done clear
  D)
          4, 5 or 6 digits done clear
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• question_answer10)
  The cube of an odd natural number is always ___.
  A)
   Even               done clear
  B)
          Odd    done clear
  C)
          Even or odd    done clear
  D)
          Can't say        done clear
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• question_answer11)
  The length of each side of a cubical box is 2.4 m. Its volume is ___.
  A)
   \[1.3824\times {{10}^{7}}cu.cm\] done clear
  B)
          \[13.824cu.cm\] done clear
  C)
          \[1.3824\times {{10}^{8}}cu.cm\] done clear
  D)
          \[1.3824\times {{10}^{4}}cu.cm\] done clear
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• question_answer12)
  The unit's digit of the cube of a number is 9. The unit's digit of its cube root is ___.
  A)
   9                                 done clear
  B)
          7         done clear
  C)
          3                                 done clear
  D)
          1         done clear
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• question_answer13)
  The cube of a number \[x\] is nine times of\[x\], then find\[x\], where \[x\ne 0\] and \[x\ne -3\].
  A)
   8                                 done clear
  B)
          2         done clear
  C)
          4                                 done clear
  D)
          3         done clear
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• question_answer14)
  Two cubes have volumes in the ratio 1:27. The ratio of the area of the face of one to that of the other is __.             
  A)
   1 : 3                done clear
  B)
          1 : 6    done clear
  C)
          1 : 9                done clear
  D)
          1 : 18  done clear
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• question_answer15)
  The smallest number by which 392 must be multiplied so that the product is a perfect cube, is ____.
  A)
   3                                 done clear
  B)
          5         done clear
  C)
          7                     done clear
  D)
          9 done clear
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• question_answer16)
  Mohit gave a problem to Samrath.

  Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number.

  Help Samrath to answer the question.
  A)
   4                                 done clear
  B)
          6                     done clear
  C)
          8                     done clear
  D)
          10                   done clear
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• question_answer17)
  A tank is in the form of a cube whose volume is \[9261000\text{ }{{m}^{3}}\]. Find the length of side of the tank
  A)
   230 m             done clear
  B)
   250 m done clear
  C)
   210 m done clear
  D)
          180 m done clear
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• question_answer18)
  Atul made a cuboid of plasticine. Length, breadth and height of the cuboid are 25 cm. 25 cm and 50 cm. How many minimum such cuboids he needs to make a perfect cube?
  A)
   4                     done clear
  B)
   20       done clear
  C)
   12                   done clear
  D)
          25       done clear
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• question_answer19)
  A rectangular cubical piece of metal of dimensions \[2\text{ }cm\text{ }\times \text{ }3\text{ }cm\text{ }\times \text{ }4\text{ }cm\] is melted. Some more of the metal is added and it is made into a cube. The cube has integral measures for its sides. What is the minimum amount of metal that is added and what is the side of this cube?
  A)
   \[10\text{ }c{{m}^{3}},\text{ }4\text{ }cm\]          done clear
  B)
   \[3\text{ }c{{m}^{3}},\text{ }3\text{ }cm\] done clear
  C)
          \[11\text{ }c{{m}^{3}},\text{ }3\text{ }cm\] done clear
  D)
          \[4\text{ }c{{m}^{3}},\text{ }3\text{ }cm\]            done clear
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• question_answer20)
  To collect rain water. Mini made a cubical tank which can hold \[91125\text{ }{{m}^{3}}\]water. She uses this water for watering the plants of her garden. What is the height of the tank?
  A)
   50 m               done clear
  B)
   25 m   done clear
  C)
   45 m   done clear
  D)
          40 m   done clear
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• question_answer21)
  Which of the following options is INCORRECT?
  A)
   Three numbers are in the ratio 1:2:3 and the sum of their cubes is 4500. The numbers will be 5, 10, 15. done clear
  B)
   The digit in the units place for the cube of a four digit number of the form \[xyz8\] is 2. done clear
  C)
   The smallest number by which 3600 be divided to make it a perfect cube is 450. done clear
  D)
   None of these done clear
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• question_answer22)
  Find the cube root of:

  (i) \[\text{0}\text{.003375 =}\underline{\text{  P }}\].

  (ii)\[\text{1}\text{.331 =}\underline{\text{  Q  }}\].

  (iii) \[\text{4}\text{.913=}\underline{\text{  R  }}\].

  (iv)\[\text{15}\text{.625=}\underline{\text{  S  }}\].

  A)

  P	Q	R	S
  0.215	1.31	2.7	2.55

  done clear
  B)

  P	Q	R	S
  0.115	1.11	1.17	3.25

                  done clear
  C)

  P	Q	R	S
  0.15	1.1	1.7	2.5

                  done clear
  D)

  P	Q	R	S
  0.25	1.21	2.17	4.15

  done clear
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• question_answer23)
  Match the following.

  Column - I	Column - II
  P. The smallest number that should be subtracted from 130 to make it perfect cube is	(i) 4
  Q. The smallest number that should be subtracted from 9268 to make it perfect cube is	(ii) 3
  R. The smallest number that should be added to 2194 to make it perfect cube is	(iii) 5
  S. The smallest number that should be added to 6855 to make it perfect cube is	(iv) 7

  A)
   P\[\to \](iii); Q\[\to \](i); R\[\to \](iv); S\[\to \](ii) done clear
  B)
   P\[\to \](ii); Q\[\to \](iv); R\[\to \](i); S\[\to \](iii) done clear
  C)
   P\[\to \](iii); Q\[\to \](i); R\[\to \](ii); S\[\to \](iv) done clear
  D)
   P\[\to \](iii); Q\[\to \](iv); R\[\to \](ii); S\[\to \](i) done clear
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• question_answer24)
  Evaluate the following.

  (i) \[\sqrt[3]{\frac{0.027}{0.008}}\div \sqrt[3]{\frac{0.729}{0.512}}-\frac{1}{3}\]

  (ii) \[\sqrt[3]{343}+\sqrt[3]{0.064}-\sqrt[3]{0.125}\]

  (iii) \[\left[ \left( \sqrt[3]{\frac{-216}{42875}}+\sqrt[3]{\frac{64}{125}} \right) \right]\times \sqrt[3]{\frac{343}{1331}}\]

  A)

  (i)	(ii)	(iii)
  1	6.9	\[\frac{2}{5}\]

                  done clear
  B)

  (i)	(ii)	(iii)
  3	7.1	\[\frac{1}{5}\]

                  done clear
  C)

  (i)	(ii)	(iii)
  4	7.9	\[\frac{2}{5}\]

                  done clear
  D)

  (i)	(ii)	(iii)
  1	6.5	\[\frac{1}{5}\]

  done clear
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• question_answer25)
  Which of the following statements is CORRECT?

  Statement 1: Cube root of 117.649 is a rational number.

  Statement 2: Cube of an odd number may or may not be odd.

  A)
   Only Statement - 1 done clear
  B)
   Only Statement - 2 done clear
  C)
   Both Statement -1 and Statement - 2 done clear
  D)
   Neither Statement -1 nor Statement - 2 done clear
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