How many cubic centimetres of iron are there in an open box whose exte

1.	How many cubic centimetres of iron are there in an open box whose external dimensions are 36cm, 25cm and 16.5cm, the iron being 1.5cm thick throughout? If 1cm3 of iron weighs 15g, find the weight of the empty box in kilograms.
Answer» The external dimensions of the box are Length = 36cm Breadth = 25cm Height = 16.5cm We know that External volume of the box = l × b × h By substituting the values External volume of the box = 36 × 25 × 16.5 So we get External volume of the box = 14850 cm³ It is given that the box is 1.5cm thick throughout Internal length of the box = (36 – (1.5 × 2)) So we get Internal length of the box = 33 cm Internal breadth of the box = (25 – (1.5 × 2)) So we get Internal breadth of the box = 22cm Internal height of the box = (16.5 – 1.5) So we get Internal height of the box = 15cm We know that Internal Volume of the box = l × b × h By substituting the values Internal Volume of the box = 33 × 22 × 15 By multiplication Internal volume of the box = 10890 cm³ So the volume of iron used in the box = External volume of box – internal volume of box By substituting the values Volume of iron used in the box = 14850 – 10890 = 3960 cm³ It is given that Weight of 1cm³ of iron = 15g = 15/1000 kg So the weight of 3960 cm³ of iron = 3960 × (15/1000) We get Weight of 3960 cm³ of iron = 59.4 kg Therefore, the volume of iron used in the box is 3960 cm³ and the weight of the empty box is 59.4 kg.

How many cubic centimetres of iron are there in an open box whose external dimensions are 36cm, 25cm and 16.5cm, the iron being 1.5cm thick throughout? If 1cm3 of iron weighs 15g, find the weight of the empty box in kilograms.

Answer»

The external dimensions of the box are

Length = 36cm

Breadth = 25cm

Height = 16.5cm

We know that

External volume of the box = l × b × h

By substituting the values

External volume of the box = 36 × 25 × 16.5

So we get

External volume of the box = 14850 cm³

It is given that the box is 1.5cm thick throughout

Internal length of the box = (36 – (1.5 × 2))

So we get

Internal length of the box = 33 cm

Internal breadth of the box = (25 – (1.5 × 2))

So we get

Internal breadth of the box = 22cm

Internal height of the box = (16.5 – 1.5)

So we get

Internal height of the box = 15cm

We know that

Internal Volume of the box = l × b × h

By substituting the values

Internal Volume of the box = 33 × 22 × 15

By multiplication

Internal volume of the box = 10890 cm³

So the volume of iron used in the box = External volume of box – internal volume of box

By substituting the values

Volume of iron used in the box = 14850 – 10890 = 3960 cm³

It is given that

Weight of 1cm³ of iron = 15g = 15/1000 kg

So the weight of 3960 cm³ of iron = 3960 × (15/1000)

We get

Weight of 3960 cm³ of iron = 59.4 kg

Therefore, the volume of iron used in the box is 3960 cm³ and the weight of the empty box is 59.4 kg.