Question

What is the volume of the sandbox that is \[1\dfrac{1}{3}\] feet tall, \[1\dfrac{5}{8}\] feet wide and \[4\dfrac{1}{2}\] feet long. How many cubic feet of sand is needed to fill the box?

Answer 1

Hint: We are given the dimensions of a sandbox as mixed fractions and we are asked to find the volume of sand required to fill the box. In other words, we have to find the volume of the given box. The given box is a cuboidal box and so the formula of the volume is \[l\times b\times h\]. We will substitute the values of the dimensions in the formula and we will have the volume of the given box and it is equal to the volume of the sand required to fill the given box. Hence, we will have the required amount of sand to fill the box.

Complete step-by-step solution:
According to the given question, we are given the dimensions of a given box and we have to find the volume of the sand required to fill the box. The given dimensions are expressed as mixed fractions and we have to first convert them to improper fractions and then calculate the required volume.
We can see that the given dimensions are all different in lengths, so the given sandbox is cuboidal in geometry.
We know that the formula of the volume of a cuboid is \[l\times b\times h\]. So, we will find the volume of the sandbox which will be equivalent to the amount of sand required to fill the sandbox.
Here,
\[l=1\dfrac{1}{3}=\dfrac{4}{3}ft\]
\[b=1\dfrac{5}{8}=\dfrac{13}{8}ft\]
\[h=4\dfrac{1}{2}=\dfrac{9}{2}ft\]
Substituting the values in the formula, we get the volume as,
Volume of the sandbox = \[l\times b\times h\]
\[\Rightarrow \dfrac{4}{3}\times \dfrac{13}{8}\times \dfrac{9}{2}\]
Multiplying the terms, we get,
\[\Rightarrow \dfrac{4\times 13\times 9}{3\times 8\times 2}\]
Cancelling out the multiples of the numbers present in the above expression, we get,
\[\Rightarrow \dfrac{13\times 3}{2\times 2}\]
\[\Rightarrow \dfrac{39}{4}\]
We get,
\[\Rightarrow 9.75f{{t}^{3}}\]
Therefore, the volume of sand required to fill the sandbox is \[9.75f{{t}^{3}}\].

Note: The volume of the sand that is required to fill the tank need not calculated again. The volume of the tank will tell us the capacity of the tank as in how much sand the tank can hold and then we can use that value while getting that particular amount of sand. Also, we figured out that the given tank is cuboidal through the dimensions given to us and only then we used the formula of the volume of a cuboid. Similarly, in many questions it may clearly state the geometry of the object, we have to understand the geometry using the dimensions given in the question.