Question

How many cubic centimetres of iron is required to construct an open box whose external dimensions are 36 cm, 25 cm and 16.5 cm provided the thickness of the iron is 1.5 cm. if one cubic cm of iron weighs 7.5 g, find the weight of the box?

Answer 1

External dimensions of the open box = 36 x 25 x 16.5 cm 

External volume of the box = 14850 cm3

Internal dimensions of the open box = (36 - 2x3.5) cm x (25 - 2x3.5) cm x (16.5 - 3.5) cm

                                                    = 29 x 18 x 13 cm
Internal volume of the box = 6786 cm3

Volume of the wood = External volume of the box - Internal volume of the box 

                              = 14850 - 6786 = 8064 cm3
Weight of 1 cubic cm of iron  = 7.5 g

Weight of 8064 cu cm of iron = 8064 x 7.5 = 60480 g = 60.48 kg.

Therefore, weight of the box = 60.48 kg.

Answer 2

External volume of the box = 36cm × 25cm × 16.5cm

= $\sf{{14850cm}^{2}}$

When the thickness of iron sheet is 1.5cm,the internal dimensions of the open iron box will be

(36-3)cm, (25-3)cm, and (16.5-1.5)cm

or 33cm ,22cm and 15cm

Internal volume of the box

= 33cm × 22cm × 15cm = $\sf{{10890cm}^{2}}$

Volume of iron used = External volume - Internal Volume

= $\sf{(14850 - 10890) {cm}^{3} }$

= $\sf{{3960cm}^{2}}$

Weight of $\sf{{1cm}^{3}}$ of iron = 7.5g

Weight of $\sf{{3960cm}^{3}}$ of iron = 7.5 × 3960g = 29700g

Hence, Weight of the box = 29.7kg