Question

A close box measures 66 cm, 36 cm and 21 cm from outside. If its walls are made of metal-sheet, 0.5 cm thick, then the capacity of the box will be
A . $40500\,\,c{m^3}$
B . $45000\,\,c{m^3}$
C . $45500\,\,c{m^3}$
D . $41500\,\,c{m^3}$

Answer 1

Hint: Since capacity of the Box is volume therefore volume of the Box will be \[length \times Breadth \times Height\]
\[Volume = length \times Breadth \times Height\]
Reducing the thickness from all the length, Breath’s and height will be the required solution.

Complete step by step solution:
External length of Box \[ = 66\,cm\]
External breath of Box\[ = 36\,cm\]
External height of box\[ = 21\,cm\]
Internal length of Box\[ = (External\,length - No.\,of\,Length\, \times Thickness)\]
Similarity Breath and Height’s
Internal length of Box\[\begin{gathered}
   = (66 - 1(2 \times 0.5)) \\
   = (66 - 1) = 65cm \\
\end{gathered} \]
Internal Breath of Box \[\begin{gathered}
   = (36 - 1(2 \times 0.5)) \\
   = (36 - 1) = 35cm \\
\end{gathered} \]
Internal Height of Box\[\begin{gathered}
   = (21 - 1(2 \times 0.5)) \\
   = (21 - 1) = 20\,cm \\
\end{gathered} \]
Internal Volume of Box\[ = 65 \times 35 \times 20 = 45500\,c{m^3}\]
Capacity of Box will be \[45500\,c{m^3}\]

So, the correct option is (c).

Note: Volume can be defined as the 3-dimension space enclosed by a boundary or occupied by an object. Finding the volume of an object can help us to determine the amount required to fill that object, like the amount of water needed to fill a bottle, an aquarium or a water tank.
The volume of an object is measured in cubic units such as cubic centimeters, cubic inch, cubic foot, cubic meter, etc. Here, for example, the volume of the cuboid or rectangular prism, with unit cubes has been determined in cubic units.
This is the Most suitable and the easiest way we mentioned in the answer.