Question

A beam \[9m\] long, \[40cm\] wide and \[20cm\] high is made up of iron which weighs \[50kg\] per cubic metre. The weight of the beam is
A. \[56{\text{ }}kg\]
B. \[48{\text{ }}kg\]
C. \[36{\text{ }}kg\]
D. \[27{\text{ }}kg\]

Answer 1

Hint: To solve this question, i.e., to get the weight of the beam, we will take the beam as a cuboid. Then firstly we will find the volume of the beam, by applying the formula of it. Then, it is given that the beam is made up of iron which weighs \[50kg\] per cubic metre. By using this condition, we will get our required answer.

Complete step-by-step answer:
We have been given a beam which is \[9m\] long, \[40cm\] wide and \[20cm\] high. It is made up of iron which weighs \[50kg\] per cubic metre. We need to find the weight of the beam.
So, length of the beam \[ = {\text{ }}9m\]
Breadth of the beam \[ = {\text{ }}40{\text{ }}cm{\text{ }} = {\text{ }}0.4{\text{ }}m\]
And, height of the beam \[ = {\text{ }}20{\text{ }}cm{\text{ }} = {\text{ }}0.2{\text{ }}m\]
Let us draw a figure, using the above information, to get a better idea of the beam.

Since, the beam is in a cuboidal shape. Therefore, to find the weight, we will apply the formula of volume of cuboid.
We know that, volume of cuboid \[ = \] Length \[ \times \] Breadth \[ \times \] Height
On putting the values in the above formula, we get
Volume of cuboidal beam =0.72m
Now, according to the question, the given beam is made up of iron which weighs \[50kg\] per cubic metre.
weight \[ = {\text{ }}50{\text{ }}kg\]
Therefore, weight of the cuboidal beam \[ = {\text{ }}0.72 \times 50{\text{ }} = {\text{ }}36{\text{ }}kg\]
So, the weight of the beam is \[36{\text{ }}kg.\] Thus, option (C)\[\;36{\text{ }}kg,\] is correct.
So, the correct answer is “Option C”.


Note: Students should notice that in the question it is nowhere mentioned that the beam is in a cuboidal shape. But we have assumed it, because we were given the length, breadth and height, and with that only cuboid shape exists. That’s why we have considered the beam to be in cuboidal shape.