Question

Find the volume of an iron bar in the shape of a cuboid whose length, breadth and height measures \[25\]cm, \[18\]cm and \[6\]cm respectively. Find the weight in kilograms if \[1\]cubic cm of iron weighs \[100\]grams.

Answer 1

Hint: Some things we need to know before solving the problem: Volume of a cuboid is given by \[l \times b \times h\] where \[l\] is the length of the cuboid, \[b\] is the breadth of the cuboid, and \[h\] is the height of the cuboid.
Conversion of kilogram into grams: \[1000\]grams \[ = \]\[1\]kilogram. While converting a smaller unit into a bigger unit we need to use division operation.

Complete step-by-step solution:

It is given that there is an iron rod which is in the shape of a cuboid. Also given that the length of that iron rod is \[25\]cm, breadth of that iron rod is \[18\]cm and the height of that iron rod is \[6\]cm.
We aim to find the volume of that iron rod which is in the shape of a cuboid. So, we have to use the volume of the cuboid formula.
We know that the volume of the cuboid is given by \[l \times b \times h\] where \[l\] is the length of the cuboid, \[b\] is the breadth of the cuboid, and \[h\] is the height of the cuboid.
We have the values of length, breadth and height. Let's substitute them in the formula.
The volume of the iron rod \[ = l \times b \times h = 25 \times 18 \times 6\]
Let us simplify it,
The volume of the iron rod \[ = 450 \times 6\]
Simplifying it further we get,
The volume of the iron rod \[ = 2700\]
Hence, the volume of the iron rod is \[2700c{m^3}\].
Thus, we have found the volume of the iron rod, now we have to find the weight of that iron rod in kilograms.
It is given that, \[1c{m^3}\] of rod weighs \[100\]grams. Thus, \[2700c{m^3} = 270000\]grams.
But we need to find the weight in kilograms, let’s convert this into kilograms.
We know that, \[1000\]grams \[ = \]\[1\]kilogram. Thus, \[270000\]grams\[ = \dfrac{{270000}}{{1000}}kg = 270kg\].
Thus, the weight of the iron rod with the volume\[2700c{m^3}\] is \[270kg\].

Note: It is given that the iron rod is in the shape of a cuboid, so it was easy for us to find the volume of the iron rod using the volume of the cuboid formula. As we know that, while doing the unit conversion, we use multiplication when we convert larger units to smaller units and division when we convert smaller units to larger units. Thus we used division to convert grams to kilograms.