question_answer

A wooden box of dimension \[8m\times 7m\times 6m\] is to carry rectangular boxes of dimensions \[8cm\times 7cm\times 6cm.\]The maximum number of boxes that can be carried in 1 wooden box is [SSC (CPO) 2014]

A) 7500000                       

B) 9800000

C) 1200000                       

D) 1000000

Correct Answer: D

Solution :

Given, a wooden box A with dimensions

\[=8m\times 7m\times 6m\]

\[=800\,\,cm\times 700\,\,cm\times 600\,\,cm\]

[as 1 m = 100cm]

Also, a wooden box 'B' with dimensions

\[=8\,\,cm\times 7\,\,cm\times 6\,\,cm\]

Now, the number of boxes of type B

which can be carried in box of type A

\[=\frac{\text{Volume}\,\,\text{of}\,\,\text{box}\,\,A}{\text{Volume}\,\,\text{of}\,\,\text{box}\,\,B}\]

\[=\frac{800\times 700\times 600}{8\times 7\times 6}=1000000\]