Question

The inside measurements of a cardboard box are \[1\dfrac{1}{2}\] m by \[\dfrac{3}{4}\] m by 60cm. How many books, 20 cm by 10 cm by 7.5 cm each can be arranged in the box.

Answer 1

Hint:
Here, in this question firstly we have to find out the total inside volume of the cardboard box. Then we have to find out the volume that is occupied by one book. Then by dividing the total inside volume of the cardboard box by the volume of each book will give us the number of books that can be arranged inside the cardboard box.

Formula used:
Volume of the cuboid \[ = l \times b \times h\] where, \[l\] is the length, \[b\] is the breadth, \[h\] is the height of the cuboid.

Complete step by step solution:
Firstly we will find out the inside volume of the cardboard box. For that we will first convert all the inside dimension of the cardboard box into centimetres and then we will find the volume of the cardboard.
We know that \[1{\rm{m}} = 100{\rm{cm}}\], so converting the dimensions, we get
\[1\dfrac{1}{2}{\rm{m}} = \dfrac{3}{2} \times 100{\rm{cm}} = 150{\rm{cm}}\]
\[\dfrac{3}{4}{\rm{m}} = \dfrac{3}{4} \times {\rm{100cm}} = 75{\rm{cm}}\]
Inside volume of the cardboard box\[ = 150 \times 75 \times 60\]
Multiplying the terms, we get
Inside volume of the cardboard box \[ = 675000{\rm{c}}{{\rm{m}}^3}\]
Now we have to find out the volume of each book. The dimension of the books is already given in centimeters. So we simply have to apply the formula of volume.
Volume of each book \[ = 20 \times 10 \times 7.5 = 1500{\rm{c}}{{\rm{m}}^3}\]
Now we will divide the total inside volume of the cardboard box by the volume of each book will give us the number of books that can be arranged inside the cardboard box.
Number of books that can be arranged inside the cardboard box
\[ = \] total inside volume of the cardboard \[/\] volume of each book
Number of books that can be arranged inside the cardboard box \[ = \dfrac{{675000{\rm{c}}{{\rm{m}}^3}}}{{1500{\rm{c}}{{\rm{m}}^3}}} = 450\]

Hence, 450 books can be arranged inside the cardboard box.

Note:
We have to convert all the given data with different units into the common unit because it will make the calculations easy otherwise it may lead to the error in calculation which will further give us the wrong answer.
It is always better to convert all the data into basic units like grams in case of weights, meters in case of lengths, seconds in case of time related problems. This conversion of the values into the basic units will make the calculations so easy and error free.
Surface area is the sum of all the areas of the faces of an object or shape and surface area is generally measured in square units. Volume is the amount of space occupied by an object in three-dimensional space. Volume is generally measured in cubic units.