Question

A covered wooden box has the inner measures as $115cm,75cmand35cm$ and thickness of wood as $2.5cm$. The volume of the wood is

• A. $85000c{m}^3$
• B. $80,000c{m}^3$
• C. $82,125c{m}^3$
• D. $84,000c{m}^3$

Answer 1

The correct option is C

$82,125c{m}^3$

Explanation for the correct option:

Finding the volume of the cuboidal box:

The inner measures of the cuboidal wooden box are $115cm,75cmand35cm$.

$\begin{array}{rcl}Volumeoftheinnercuboidalbox& =& l\times b\times h\\ & =& 115\times 75\times 35\\ & =& 301875c{m}^3\end{array}$

The thickness of the wooden box is $2.5cm$, then the dimension of the outer box will be increased by $2.5cm$ from both side,

length =$115+2\times 2.5=120cm$

breadth = $75+2\times 2.5=80cm$

height = $35+2\times 2.5=40cm$

$\begin{array}{rcl}Volumeoftheoutercuboidalbox& =& l\times b\times h\\ & =& 120\times 80\times 40\\ & =& 384000c{m}^3\end{array}$

Hence

$\begin{array}{rcl}Thevolumeofawood& =& Externalvolume–InternalvolumeV\\ & =& 384000c{m}^3–301875c{m}^3\\ & =& 82125c{m}^3\end{array}$

Hence, option B is correct.