Question

Find the volume of iron required to make an open box whose external dimensions are 36 cm × 25 cm × 16.5 cm, the box being 1.5 cm thick throughout. If 1 cm³ of iron weighs 8.5 grams, find the weight of the empty box in kilograms.

Answer 1

External length = 36 cm
External width = 25 cm
External height = 16.5 cm

External volume of the box$=36\times 25\times 16.5=14850{\text{cm}}^3$

Thickness of iron = 1.5 cm

∴ Internal length $=36-(1.5\times 2)=33$ cm
Internal width $=25-(1.5\times 2)=22$ cm
Internal height $=16.5-1.5=15$ cm (as the box is open)

Internal volume of the box$=33\times 22\times 15=10890{\mathrm{cm}}^3$

Volume of iron = External volume − Internal volume$=14850-10890=3960{\text{cm}}^3$

Given:
${\text{1 cm}}^3\text{of iron}=8.5\text{grams}$

Total weight of the box $=3960\times 8.5=33660\mathrm{grams}=33.66\mathrm{kilograms}$