Question

Small butter cubes have a side measuring \[10cm\]. How many such cubes can be placed in a cardboard box of dimensions \[35cm{\text{ }} \times {\text{ }}20cm{\text{ }} \times {\text{ }}20cm\] ?

Answer 1

Hint: In the given question, we have been asked to find the number of cubes that can be placed in a cardboard box. In order to proceed with the following question we need to find the volume of cardboard and volume of cubes, and then divide them. Volume is basically the space inside any 3-D figure. Cardboard is cuboid in shape. Volume of cardboard is the product of length, width and height. Volume of cube is $side \times side \times side$

Formula used: Volume of cube = $side \times side \times side$
Volume of cardboard = $length \times width \times height$

Complete step by step solution:
We are given,
Dimensions of cardboard box = \[35cm{\text{ }} \times {\text{ }}20cm{\text{ }} \times {\text{ }}20cm\]
Side of cube = \[10cm\]
To find number of cubes that can be placed, we need to find
Volume of cardboard = \[35cm{\text{ }} \times {\text{ }}20cm{\text{ }} \times {\text{ }}20cm\]
$ \Rightarrow 14000c{m^3}$
Volume of cube = $side \times side \times side$
$ \Rightarrow 10cm \times 10cm \times 10cm$
$ \Rightarrow 1000c{m^3}$
Number of cubes that can be placed = $\dfrac{{Volume\;of\;cardboard}}{{Volume\;of\;cube}}$
Since both the terms are of same unit, they can be divided.
$ \Rightarrow \dfrac{{14000}}{{1000}}$
$ \Rightarrow 14\;cubes$
This is the required answer.

Note: While calculating volume, you need to take care of units of values. Units which are used in formulas should be the same. For example- if you measure height in inches then length should also be in inches. Volume can only be calculated of 3-D figures, not of 2-D figures. We need to carefully examine the units while dividing two terms, terms can only be divided when they are in the same unit, if they are not then change them into the same unit.