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.
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.

Let the length (l), breath (b), and stature (h) be the outside element of an open box and thickness be x.

NCERT Exemplar Class 10 Maths Chapter 12 Ex. 12.4 Question 3

The volume of metal utilized in box = Volume of outer box – Volume of inner box

Think about outside box,

Length, l = 36 cm

 

Broadness, b = 25 cm

Tallness, h = 16.5 cm

We realize that the condition of the volume of cuboid is given by,

Volume of cuboid = lbh, where, l, b and h are the length, expansiveness and stature of tank separately

Volume of outer box \[=\text{ }36\left( 25 \right)\left( 16.5 \right)\text{ }=\text{ }14850\text{ }cm3\]

Since the crate is open from top,

Think about inside box,

The thickness of different sides is diminished as follows,

Length, l’ = Length of outer box – 2(thickness of box) \[=\text{ }36\text{ }\text{ }2\left( 1.5 \right)\text{ }=\text{ }33\text{ }cm\]

Expansiveness, b’ = Breadth of outside box – 2(thickness of box)\[=\text{ }25\text{ }\text{ }2\left( 1.5 \right)\text{ }=\text{ }22\text{ }cm\]

Stature, h’ = Height of outside box – thickness of box \[=\text{ }16.5\text{ }\text{ }1.5\text{ }=\text{ }15\text{ }cm\]

Volume of inside box = 33(22)(15) = 10890

Furthermore,

Volume of metal in box \[=\text{ }14850\text{ }\text{ }10890\text{ }=\text{ }3960\text{ }cm3\]

We realize that,

1 cm3 weighs 7.5 g

Thus, 3960 cm3 weighs 3960(7.5) = 29,700 g

Consequently, the heaviness of box is 29,700 g for example 29.7 kg