Question

The four walls and ceiling of a room are to be repaired. The length and breadth of the room are 8 meter and 4 meter respectively and its height is 3 meter. Find the cost of repair at Rs. 30 per meter2.
(a). Rs. 3100
(b). Rs. 3110
(c). Rs. 3120
(d).Rs. 3121

Answer 1

Hint:- The formula that we are going to use to calculate the area of the whole room would be:-
\[=2\text{ }\left( l\text{ }+\text{ }b \right)\text{ }h\text{ }+\text{ }l\times b\]
Here ‘l’ stands for the length of the room.
And ‘b’ stands for the breadth of the room.
While ‘h’ stands for the height of the room.
And then, we will multiply the answer by 30.

Complete step-by-step solution -

So, let us calculate the area of the whole room.
We know that the length of the room is 8 meter, the breadth of the room is 4 meter and the height of the room is 3 meter.
Let us now substitute the measures of the length, breadth and height of the room in the formula.
\[\begin{array}{*{35}{l}}
   =2\text{ }\left( l\text{ }+\text{ }b \right)\text{ }h\text{ }+\text{ }l\times b \\
   =2\text{ }\left( 8\text{ }+\text{ }4 \right)\text{ }3\text{ }+\text{ }8\text{ }\times \text{ }4 \\
   =2\text{ }\left( 12 \right)\text{ }3\text{ }+\text{ }8\text{ }\times \text{ }4 \\
   =24\text{ }\times \text{ }3\text{ }+\text{ }32 \\
   =72\text{ }+\text{ }32 \\
   =104\text{ }{{m}^{2}} \\
\end{array}\]
So, the area of the room is 104 square meters.
Let us now calculate the cost to repair the room at Rs. 30 per square meter.
\[104\times 30\text{ }=\text{ }Rs.\text{ }3120\]
Therefore, the cost of repairing the room at the cost of Rs. 30 per square meter is Rs. 3120.
Hence, the answer of this question is (c) Rs. 3120.

Note:-It is very important to do all the calculations very carefully as if there is any mistake in the calculus; the answer can come out to be wrong.
Let us now understand the reason behind using the following formula for solving this question:-
\[=2\text{ }\left( l\text{ }+\text{ }b \right)\text{ }h\text{ }+\text{ }l\times b\]
As we have to calculate the area of only the four walls and the ceiling of the room, and not the floor, therefore, we used this formula.
Also, to calculate the area of just the four walls of a room, the formula that we use is \[2(l+b)h\] . And, to calculate the area of the ceiling, we have to multiply the length and breadth of the ceiling, as this is the very formula that we use to calculate the area of a rectangle, and the shape of the ceiling is also rectangular.
Therefore, we used this formula:-
\[=2\text{ }\left( l\text{ }+\text{ }b \right)\text{ }h\text{ }+\text{ }l\times b\]