Q. 24.8( 4 Votes )

Sumanta has made

Answer :

Given that,

Sumanta has made many cubes of length, 1 cm.


This means, volume of each cube = length × length × length


Here, length = 1 cm


Volume of each cube = 1 × 1 × 1 cm3


Volume of each cube = 1 cm3


And a single cube out of those many cubes is made by Manami.


Let us assume that Sumanta has made ‘Z’ cubes of length 1 cm, where Z is some natural number.


So, if volume of 1 cube = 1 cm3


Volume of Z cubes = Z × 1 cm3


Volume of Z cubes = Z cm3


We have volumes of cube in the options.


(i). Let us check for 100.


We need to find cube root of 100. If we are able to find the cube root of 100, then we can say that a big cube is possible in this case.


100 = 2×2× 5× 5


We can see 100 cannot be written as a perfect cube.


100 ≠ (any integer)3


Since, we have cubes of length 1 cm each.


So, length of the final big cube will also be a natural number.


And cube root of 100 is not a natural number.


Thus, Manami won’t be able to make a big cube in this case.


(ii). Let us check for 1000.


We need to find the cube root of 1000. If we are able to find the cube root of 1000, then we can say that a big cube is possible in this case.


Cube root of 1000


1000 = 10× 10× 10


Cube root of 1000 = (1000)1/3


= 10


Since, we have cubes of length 1 cm each.


So, length of the final big cube will also be a natural number.


And cube root of 1000 is a natural number.


Thus, Manami will be able to make a big cube in this case.


(iii). Let us check for 1331.


We need to find the cube root of 1331. If we are able to find the cube root of 1331, then we can say that a big cube is possible in this case.


Cube root of 1331


1331 = 11× 11× 11


Cube root of 1331 = (1331)1/3


= 11


Since, we have cubes of length 1 cm each.


So, length of the final big cube will also be a natural number.


And cube root of 1331 is a natural number.


Thus, Manami will be able to make a big cube in this case.


(iv). Let us check for 1210.


We need to find the cube root of 1210. If we are able to find the cube root of 1210, then we can say that a big cube is possible in this case.


Cube root of 1210


1210 = 2× 5× 11× 11


We can see 1210 cannot be written as a perfect cube.


1210 ≠ (any integer)3


Since, we have cubes of length 1 cm each.


So, length of the final big cube will also be a natural number.


And cube root of 1210 is not a natural number.


Thus, Manami will not be able to make a big cube in this case.


(v). Let us check for 3375.


We need to find the cube root of 3375. If we are able to find the cube root of 3375, then we can say that a big cube is possible in this case.


Cube root of 3375


3375 = 15× 15× 15


Cube root of 3375 = (3375)1/3


= 15


Since, we have cubes of length 1 cm each.


So, length of the final big cube will also be a natural number.


And cube root of 3375 is a natural number.


Thus, Manami will be able to make a big cube in this case.


(vi). Let us check for 2700.


We need to find the cube root of 2700. If we are able to find the cube root of 2700, we can say that a big cube is possible in this case.


Cube root of 2700


2700 = 3× 3× 3× 2× 2× 5× 5


We can see 2700 cannot be written as a perfect cube.


2700 ≠ (any integer)3


Since, we have cubes of length 1 cm each.


So, length of the final big cube will also be a natural number.


And cube root of 2700 is not a natural number.


Thus, Manami will not be able to make a big cube in this case.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Smart Revision | Revision of Cubes and Cube RootsSmart Revision | Revision of Cubes and Cube RootsSmart Revision | Revision of Cubes and Cube Roots47 mins
Quiz | Cubes and Cube RootsQuiz | Cubes and Cube RootsQuiz | Cubes and Cube Roots41 mins
Quiz | Cubes and Cube RootsQuiz | Cubes and Cube RootsQuiz | Cubes and Cube Roots43 mins
Quiz | Cubes and Cube RootsQuiz | Cubes and Cube RootsQuiz | Cubes and Cube Roots41 mins
Extra Qs. of Cubes and Cube RootsExtra Qs. of Cubes and Cube RootsExtra Qs. of Cubes and Cube Roots43 mins
Smart Revision | Cubes and Cube RootsSmart Revision | Cubes and Cube RootsSmart Revision | Cubes and Cube Roots46 mins
NCERT | Imp. Qs. on Cubes and Cube RootsNCERT | Imp. Qs. on Cubes and Cube RootsNCERT | Imp. Qs. on Cubes and Cube Roots47 mins
Champ Quiz | Cubes and Cube RootsChamp Quiz | Cubes and Cube RootsChamp Quiz | Cubes and Cube Roots33 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses
RELATED QUESTIONS :

Let us write the West Bengal - Mathematics

Let us calculate West Bengal - Mathematics

Let us calculate West Bengal - Mathematics

Let us write whicWest Bengal - Mathematics

Debnath has made West Bengal - Mathematics

Let's find perfecWest Bengal - Mathematics

Let’s form two cuWest Bengal - Mathematics

Sumanta has made West Bengal - Mathematics