Question

The length of the wall is 8m and height is 4m. Wall is 35 cm thick. There is one door of size \[2m\times 1m\] and two windows of size \[1.2m\times 1m\]. Find the expenditure of making the wall at the rate of Rs. 1500 per cubic meter.

Answer 1

Hint: Calculate the volume of the wall and subtract this from the space occupied by doors and windows.
\[Volume\text{ }=length\times width\times thickness.\]

Complete step by step answer:
Given, the length of wall is 8m and height of wall is 4m and thickness is 35cm that is 0.35m. Consider the diagram:

Therefore, the actual volume of the wall is 8×4×0.35=11.2 cubic meters.
Now, the door has dimensions of 2m×1m and it will occupy the thickness that is equal to the thickness of the wall because the door is through the wall. So, the dimensions of the door are 2m×1m×0.35m.
Therefore, door occupies a volume of
\[~2\times 1\times 0.35=0.70\]cubic meters.
The wall has two windows of dimensions \[1.20m\times 1m\]and it will occupy the thickness that is equal to the thickness of the wall because the windows are through the walls. So, the dimensions of windows are \[1.20\times 1m\times 0.35m.\]
Therefore, the volume occupied by windows is \[2\left( 1.20\times 1\times 0.35 \right)=0.84\]cubic meters because there are two windows.

We have expenditure on the volume of \[\left( 11.2-0.70-0.84 \right)=9.66\]cubic meters because the volume occupied by doors and windows is left for their construction.

Given, the expenditure for making the wall is Rs.1500 per cubic meter.
The volume of the wall to be constructed is 9.66 cubic meters.
Therefore, expenditure for constructing the wall is \[\left( \text{ }9.66\times 1500 \right)rupees\text{ }=14,490\]rupees.
Hence, the expenditure for making the wall is 14,490 rupees.

Note: Students must take care while converting m to cubic meters. This may lead to the get wrong answers which may vary with the point. Here, thickness also included, so pay attention while doing the sum.