Question

The external dimensions of a closed wooden box are 48 cm, 36 cm, 30 cm, The box 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?

Answer 1

Outer dimensions of a closed wooden box = 48 cm $\times$ 36 cm $\times$ 30 cm
Thickness of wood = 1.5 cm.
$\therefore$ Inner length (l) =$48-2\times 1.5cm=48-3=45cm$
Breadth (b) = 36 - 2 $\times$ 1.5 = 36-3 = 33 cm
Height (h) = 30-2 $\times$ 1.5 = 30 -3 = 27 cm
$\therefore$ Volume of inner box = $l\times btimesh$
= $45\times 33\times 27c{m}^3=40095c{m}^3$
Volume of one brick of size 6 cm $\times$ 3 cm $\times$ 0.75 cm
= $6\times 3\times 0.75=6\times 3\times \frac{3}{4}c{m}^3=\frac{27}{2}c{m}^3$
$\therefore$ Number of bricks = $\frac{40095\times 2}{27}$
= 1485 $\times$ 2 = 2970 bricks