The external dimensions of a closed wooden box are $48\ cm, 36\ cm, 30\ cm$. The box is made of $1.5\ cm$ thick wood. How many bricks of size $6\ cm \times 3\ cm \times 0.75\ cm$ can be put in this box?

Given:

The external dimensions of a closed wooden box are $48\ cm, 36\ cm, 30\ cm$. The box is made of $1.5\ cm$ thick wood.

To do:

We have to find the number of bricks of size $6\ cm \times 3\ cm \times 0.75\ cm$ that can be put in this box.

Solution:

External length of the closed wooden box $(L) = 48\ cm$

External width of the box $(B) = 36\ cm$

External height of the box $(H) = 30\ cm$

Thickness of the wood $= 1.5\ cm$

This implies,

Internal length of the box $(l) = 48 - 2 \times 1.5$

$= 48 - 3$

$= 45\ cm$

Internal width of the box $(b) = 36 - 2 \times 1.5$

$= 36 - 3$

$= 33\ cm$

Internal height of the box $(h) = 30 - 2 \times 1.5$

$= 30 - 3$

$= 27\ cm$

The volume of the internal box $= lbh$

$= 45 \times 33 \times 27$

Volume of one brick $= 6 \times 3 \times 0.75$

$=\frac{18 \times 75}{100}$

$=\frac{27}{2} \mathrm{~cm}^{3}$

Therefore,

Number of bricks that can be put in the box $=\frac{45 \times 33 \times 27\times2}{27}$

$=2970$

Tutorialspoint

e

Updated on: 10-Oct-2022

52 Views

Kickstart Your Career

Get certified by completing the course

Get Started