Question

The capacity of a closed wooden box of thickness $ 1\;cm $ and of dimensions $ 32\;cm\; \times \;20\;cm\; \times \;17\;cm $ is
A. $ 10880\;c{m^3} $
B. $ 69\;c{m^3} $
C. $ 8100\;c{m^3} $
D. $ 8000\;c{m^3} $

Answer 1

Hint: We have been given the dimensions of a wooden box. These dimensions are the outer length, breadth, height and thickness of the wooden box. The capacity of a box is measured as the volume of the empty box at the inner side. In other words we can say that the capacity of a box is the volume of any substance that the box can hold. Since a box holds the substance in the inner side, we calculate the volume using the inner dimensions, i.e. outer dimension minus the thickness.

Complete step by step solution:
We have been given the dimensions of a wooden box as $ 32\;cm\; \times \;20\;cm\; \times \;17\;cm $ . This is the length, breadth and the height of the box from the outer side. We are also given the thickness of the box as $ 1\;cm $ .
We have to find the capacity of the box. The capacity of the box is the inner volume of the box.
The inner dimensions of the box can be found by subtracting the thickness from the outer dimensions. We will subtract twice the thickness in each dimension since the thickness is on both sides of the dimensions.
Thus,
 $
  Inner\;length\; = \;Outer\;length\; - \;\left( {2 \times Thickness} \right) = 32 - \left( {2 \times 1} \right) = 32 - 2 = 30\;cm \\
  Inner\;breadth\; = \;Outer\;breadth\; - \;\left( {2 \times Thickness} \right) = 20 - \left( {2 \times 1} \right) = 20 - 2 = 18\;cm \\
  Inner\;height\; = \;Outer\;height\; - \;\left( {2 \times Thickness} \right) = 17 - \left( {2 \times 1} \right) = 17 - 2 = 15\;cm \\
  $
Thus, the capacity can be found as,
 $ Capacity = Inner\;Volume = 30\;cm \times 18\;cm \times 15\;cm $
We can multiply and find the capacity as,
 $ Capacity = 30\;cm \times 18\;cm \times 15\;cm = 8100\;c{m^3} $
Hence, option (C) is the correct answer.
So, the correct answer is “Option C”.

Note: Since we were given the outer dimensions, we had to find the inner dimensions to find the capacity. We find the inner dimensions by subtracting twice the thickness in the outer dimensions. In this question we were given a closed box, but when we are given an open box we subtract the thickness only once in the outer height.