Question

How many cubic centimetres of iron are there in an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm, the iron being 1.5 cm thick throughout? If 1 cubic cm of iron weighs 15 g, find the weight of the empty box in kg.

Answer 1

$\text{External length of open box (L)}=36cm$

$\text{Breadth (B)}=25cm$

$\text{and Height (H)}=16.5cm$

$\text{Width of iron sheet used}=1.5cm$

$\therefore \text{Inner length (l)}=36-1.5\times 2$

$=36-3=33cm$

$\text{Breadth (b)}=25-2\times 1.5$

$=25-3=22cm$

$\text{and Height (h)}=16.5-1.5=15cm$

$\therefore \text{Volume of the iron used}$

$=\text{Outer volume - Inner volume}$

$=36\times 25\times 16.5-33\times 22\times 15$

$=14850-10890=3960c{m}^3$

$\text{Weight of 1}c{m}^3=15g$

$\therefore \text{Total weight}=\frac{3960\times 15}{1000}=\frac{59400}{1000}kg$

$=59.4kg$