A box without a lid is made of wood which is 3 cm thick Its external dimensions are 86 - Maths - Mensuration

Question

A box without a lid is made of wood which is 3 cm thick Its
external dimensions are 86 cm x 60 cm x 45 cm Find:
1 the capacity of the box in cubic centimetres,
2 the volume of wood used in making the box, and
3 the weight of the empty box,if 1 cubic centimetre of wood
weighs 0 8 grams

Ayush Jha · Accepted Answer

We have a cuboidal box with external dimensions (86cm x 60m x 45m).

The thickness of the wood in the box is 3 cm.

The box is open from one end.

Therefore the internal dimensions are (80cm x 54cm x 42cm) as the box is considered to be open along its height at one end

1> The capacity of the box can be calculated as-

$= (l) (b) (h) = (80) (54) (42) = 181440 {c m}^{3}$

2> Volume of wood used in the box can be calculated as-

$= E x t e r n a l V o l u m e - I n t e r n a l V o l u m e = [(86) (60) (45) - (80) (54) (42)] = (232200 - 181440) {c m}^{3} = 50760 {c m}^{3}$

3> Density of wood is 0.8 $g m / {c m}^{3}$ .

We know that,

Mass=Density x Volume

So, weight of the empty box is-

$M a s s = (0.8) (50760) g m = 40608 g m = 40.608 k g$