Question

A room is in the form of a cuboid of measures 50m ×13m × 20m. How many cuboidal boxes can be stored in it if the volume of one box is $0.6m^3$?

a.40,000

b.30,000

c.50,000

d.None of these

Answer 1

Hint: Mathematics includes the study of topics which are related to quantity, structure, space and change. It has no generally accepted definition. To specify a figure most fundamental quantities are perimeter, area and volume. Perimeter can be defined as the total length of the boundary of a geometrical figure. Area can be defined as the space occupied by a flat shape or the surface of an object. Volume can be defined as the 3-dimensional space enclosed by a boundary or occupied by an object. This implies that using this definition we can easily solve our problem.

 Complete step-by-step answer:
Mathematics related to all the phenomena occurring in the world. When mathematical structures are good models of real phenomena mathematical reasoning can be used to provide insight or predictions about nature. There are several types of operators which are available in mathematics. To specify a figure most fundamental quantities are perimeter and area. Volume can be defined as the total length of the boundary of a geometrical figure. For example, the volume of a cube is the cube of its length of side.

For our problem, we have a cuboid whose width, length and height are given. All the sides are perpendicular to each other.

This implies that the volume of cuboid can be specified by the product of length, width and height.

This can be represented in mathematical expression as: $V=l\times b\times h$
     \[\]
where l be the length, b be the breadth and h be the height of the cuboid.

The cuboid has dimensions as 50m, 30m and 20m which means length is 50m, breadth is 30m and height is 20m.

This implies that the volume will be:
$\begin{align}
  & V=50\times 30\times 20 \\
 & V=30000{{m}^{3}} \\
\end{align}$

Volume of the cuboid measuring $50\times 30\times 20=30000{{m}^{3}}$.

As per the question, the volume of one small box is 0.6 m3.

Number of cuboidal boxes stored in the big cuboid is:
$\dfrac{Volume\text{ of cuboid}}{Volume\text{ of one small box}}=\dfrac{30000{{m}^{3}}}{0.6{{m}^{3}}}$

Number of cuboidal boxes$=50000$.

Therefore, the correct option is option (c).

Note: The key step for solving this problem is the knowledge of volume of a cuboid. If we want to fix a small body inside a large body, then the volume of both the bodies must be equal. By using this fact, we calculated the total number of boxes which can easily be accommodated in the cuboid.