Question

A cuboidal container has a dimension of $20\,cm\,\, \times 18\,cm\,\, \times 16cm\,$. Find the maximum number of syrup bottles whose contents can be emptied into the container, if each bottle contains $24\,c{m^3}$ of syrup.
A) $120$
B) $180$
C) $240$
D) $270$

Answer 1

Hint: To evaluate the numbers of syrups bottles first, evaluate the volume of the cuboidal container which is the product of length, breadth and height. After that divide the total volume by the volume of each bottle of syrup.

Complete step-by-step answer:
We are given that the cuboidal container has a dimension of $20\,cm\,\, \times 18\,cm\,\, \times 16cm\,$and syrup bottles and each bottle contain $24\,c{m^3}$of syrup.
We have to find the maximum number of syrup bottles whose contents can be emptied into the container.
First, we evaluate the volume of the given cuboidal container.
We know that the volume of any cuboid shape is the product of length, breadth and height.
In our case, the volume is given in the multiplication form; we have to just solve it.
Let the volume of the cuboidal container is V.
Evaluate the product.
\[
  V = 20 \times 18 \times 16 \\
  V = 5760\,c{m^3} \\
 \]
Now, we have the quantity of syrup that each syrup bottle contains which is $24\,c{m^3}$ and our total volume of the cuboidal container is $5760\,c{m^3}$.
In order to evaluate the maximum numbers of syrup bottles, we have to divide the volume of the cuboidal container by the quantity of syrup that each syrup bottle contains.
Let the maximum number of bottles be N.
$
  N = \dfrac{{5760}}{{24}} \\
  N = 240 \\
 $

Hence, the maximum number of bottles is $240$. Therefore, Option (C) is correct.

Note:
The most important thing in these types of questions is the unit of the shapes. Don’t forget to make the units the same if they are different and then proceed with the solution.
Short trick: When there are two volumes of shapes in the question and have asked about the number of quantities then just simply divide the larger volume by smaller volume.