Question

A trunk measures \[48{\text{ inches}}\] long, \[22\dfrac{1}{2}{\text{ feet}}\] wide, and \[32{\text{ inches}}\] high. What is the volume of the box?

Answer 1

Hint: In the question we are asked to find the volume of the box so, to find that we will multiply the length, breadth and the height of the trunk. But before finding the volume, as we can see that the length, breadth and height are in different units, we will convert them into the same units and then we will find the volume.

Complete step by step answer:
Given,
Length \[{\text{ = 48 inches}}\]
Width \[{\text{ = 22}}\dfrac{1}{2}{\text{ feet}}\]
Height \[{\text{ = 32 inches}}\]
As we can see that the length and height are in the same units but, the width is in different units. So, we will convert the width into the same units as length and height.
We know;
\[1{\text{ ft = 12 in}}\]
\[ \Rightarrow 22\dfrac{1}{2}{\text{ ft = 12}} \times {\text{22}}\dfrac{1}{2}{\text{ in}}\]
On calculation we get;
\[ \Rightarrow 22\dfrac{1}{2}{\text{ ft = 12}} \times \dfrac{{45}}{2}{\text{ in}}\]
On multiplication we get;
\[ \Rightarrow 22\dfrac{1}{2}{\text{ ft = 270 in}}\]
Now we have all the dimensions in the same unit. So, now we will find the volume.
Volume of the box \[ = {\text{ length }} \times {\text{width }} \times {\text{height}}\]
Putting the values, we get;
Volume of the box \[ = \left( {48 \times 270 \times 32} \right){\text{ i}}{{\text{n}}^3}\]
On calculating we get;
Volume of the box \[{\text{ = 414,720 i}}{{\text{n}}^3}\]

Note: One thing to note is that we can also solve the question by changing the length and height into feet.
But there we will need to convert two dimensions so, to avoid that, what we can do is we can get the answer in inches and in the last we can convert cubic inch to cubic feet. One mistake that the students make is that they forget to put the units of volume in the final answer.