Question

An oil container measuring 75 cm by 60 cm by 42 cm is half full of oil. Find the volume of oil in the container.

Answer 1

Hint:
 We are given a container in the shape of cuboids whose dimensions are $ 75\times 60\times 42 $. So, we consider length as 75, breadth as 60, and height as 42. Then we first find the volume of the container. As the container is cuboid so we use $ v=l\times b\times h $. Once we had the volume of the container than as oil is half
So volume of oil $ =\dfrac{\text{Volume of box}}{2} $
Then we will solve and find the required answer.

Complete step by step answer:
We are given an oil container which is filled with oil.
We are given dimensions of 75 by 60 by 42 cm.
Now, firstly we see that the dimensions of the box are all different. So from the figure, we can be sure that our box is a cuboid.
Now we know that in any cube there are 3 dimensions which are defined as length, breadth, and height.
We are given that our box measure as –
75 cm by 60 cm by 42 cm. So we can consider that –
We have a length as 75 cm, breadth as 60 cm, and height as 42 cm.
Means we have $ l=75cm,b=60cm\text{ and h=42cm} $

Now we are asked to find the volume of the oil container.
As we got that container is in the shape of cuboids with $ l=75cm,b=60cm\text{ and h=42cm} $ .
We know the volume of cuboids is given as –
 $ v=l\times b\times h $
Now, as $ l=75cm,b=60cm\text{ and h=42cm} $
So, we get –
 $ v=75\times 60\times 42 $
 $ =4500\times 42 $
Simplifying further, we get –
 $ v=189000c{{m}^{3}} $
So we have that the volume of the whole box is $ 189000c{{m}^{3}} $ .
As we have that the oil is filled up to half the container
So, Volume of oil $ =\dfrac{\text{Volume of container}}{2} $
As volume of container $ =18900 $
And volume of oil $ =\dfrac{189000}{2} $
So, we get –
Volume of oil $ =94500c{{m}^{3}} $ .
Required answer is $ 94500c{{m}^{3}} $ .
Note:
For cuboids volume is product of lbh, where its dimension is $ l\times b\times h $ . For cube volume is given as $ \text{side}\times \text{side}\times \text{side} $ that is $ {{\left( \text{side} \right)}^{3}} $ . Remember here length, breadth and height is not given. So, we can consider any term as length or breadth or height.