Answer
423.9k+ views
Hint: First of all considering the unit conversion that \[{\text{1m = 100cm}}\]and calculating the volume of both the cubes and then diving the volume of a bigger cube by smaller cube to get an exact number of cubes that can be inserted into the bigger one.
Complete step by step answer:
As per the given that one cube is of \[{\text{10cm}}\] edge and another is of \[{\text{1m}}\] edge
Volume of cube (side length as a) \[{\text{ = }}{{\text{a}}^{\text{3}}}\]
So, now converting all into similar units.
As \[{\text{1m = 100cm}}\],
So the volume of the larger cube is
\[
{\text{V = }}{{\text{a}}^{\text{3}}} \\
{\text{ = (100)(100)(100)}} \\
{\text{ = 1000000c}}{{\text{m}}^{\text{3}}} \\
\]
And the volume of a smaller cube is
\[
{\text{V = }}{{\text{a}}^{\text{3}}} \\
{\text{ = (10)(10)(10)}} \\
{\text{ = 1000c}}{{\text{m}}^{\text{3}}} \\
\]
Now, to calculate the number of the smaller cube that can be inserted into the larger cube is given by
\[
{\text{1000n = 1000000}} \\
\therefore {\text{n = }}\dfrac{{1000000}}{{1000}} \\
{\text{n = 1000}} \\
\]
Hence, option (c) is our required correct answer.
Note: In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meetings at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. The volume of a cube is found by multiplying the length of any edge by itself thrice.
Complete step by step answer:
As per the given that one cube is of \[{\text{10cm}}\] edge and another is of \[{\text{1m}}\] edge
Volume of cube (side length as a) \[{\text{ = }}{{\text{a}}^{\text{3}}}\]
So, now converting all into similar units.
As \[{\text{1m = 100cm}}\],
So the volume of the larger cube is
\[
{\text{V = }}{{\text{a}}^{\text{3}}} \\
{\text{ = (100)(100)(100)}} \\
{\text{ = 1000000c}}{{\text{m}}^{\text{3}}} \\
\]
And the volume of a smaller cube is
\[
{\text{V = }}{{\text{a}}^{\text{3}}} \\
{\text{ = (10)(10)(10)}} \\
{\text{ = 1000c}}{{\text{m}}^{\text{3}}} \\
\]
Now, to calculate the number of the smaller cube that can be inserted into the larger cube is given by
\[
{\text{1000n = 1000000}} \\
\therefore {\text{n = }}\dfrac{{1000000}}{{1000}} \\
{\text{n = 1000}} \\
\]
Hence, option (c) is our required correct answer.
Note: In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meetings at each vertex. The cube is the only regular hexahedron and is one of the five Platonic solids. The volume of a cube is found by multiplying the length of any edge by itself thrice.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Why Are Noble Gases NonReactive class 11 chemistry CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let X and Y be the sets of all positive divisors of class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x and y be 2 real numbers which satisfy the equations class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x 4log 2sqrt 9k 1 + 7 and y dfrac132log 2sqrt5 class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Let x22ax+b20 and x22bx+a20 be two equations Then the class 11 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
At which age domestication of animals started A Neolithic class 11 social science CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Which are the Top 10 Largest Countries of the World?
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Give 10 examples for herbs , shrubs , climbers , creepers
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Difference Between Plant Cell and Animal Cell
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Write a letter to the principal requesting him to grant class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Change the following sentences into negative and interrogative class 10 english CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)
Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE
![arrow-right](/cdn/images/seo-templates/arrow-right.png)