Answer
Verified
388.2k+ 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
The branch of science which deals with nature and natural class 10 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
Define absolute refractive index of a medium
Find out what do the algal bloom and redtides sign class 10 biology CBSE
Prove that the function fleft x right xn is continuous class 12 maths CBSE
Find the values of other five trigonometric functions class 10 maths CBSE
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
How do you solve x2 11x + 28 0 using the quadratic class 10 maths CBSE
Select the correct plural noun from the given singular class 10 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The sum of three consecutive multiples of 11 is 363 class 7 maths CBSE
What is the z value for a 90 95 and 99 percent confidence class 11 maths CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
How many squares are there in a chess board A 1296 class 11 maths CBSE