### Solution
Given:
- The area of the four walls of the room is [tex]\( 88 \, \text{sq. meters} \)[/tex].
- Length ([tex]\( \ell \)[/tex]) = [tex]\( 6 \, \text{meters} \)[/tex]
- Breadth ( [tex]\( b \)[/tex]) = [tex]\( 5 \, \text{meters} \)[/tex]
- The room has one door with an area of [tex]\( 3 \, \text{sq. meters} \)[/tex].
- The room has two windows, each with an area of [tex]\( 2.25 \, \text{sq. meters} \)[/tex].
- The cost of painting per square meter = Rs [tex]\( 175 \)[/tex].
We'll solve this problem step by step.
### (a) Formula to calculate the area of four walls
The area of the four walls of a cuboid can be calculated using the formula:
[tex]\[ 2h(\ell + b) \][/tex]
Here, [tex]\( h \)[/tex] is the height of the room, [tex]\( \ell \)[/tex] is the length, and [tex]\( b \)[/tex] is the breadth.
Therefore, the correct formula is:
[tex]\[ (C) \, 2h(\ell + b) \][/tex]
### (b) Finding the height of the room
Given:
[tex]\[ 2h(\ell + b) = 88 \][/tex]
We need to find [tex]\( h \)[/tex].
Plug in the given values:
[tex]\[ 2h(6 + 5) = 88 \][/tex]
[tex]\[ 2h \cdot 11 = 88 \][/tex]
[tex]\[ 22h = 88 \][/tex]
[tex]\[ h = \frac{88}{22} = 4 \][/tex]
So, the height of the room is [tex]\( 4 \, \text{meters} \)[/tex].
### (c) Total cost of painting the walls excluding the door and windows
First, calculate the total area excluding the door and windows.
- Total area of the door = [tex]\( 3 \, \text{sq. meters} \)[/tex]
- Total area of the windows = [tex]\( 2 \times 2.25 = 4.5 \, \text{sq. meters} \)[/tex]
Thus, the total area to be excluded = [tex]\( 3 + 4.5 = 7.5 \, \text{sq. meters} \)[/tex]
Total area to be painted:
[tex]\[ 88 - 7.5 = 80.5 \, \text{sq. meters} \][/tex]
Now, calculate the total cost:
[tex]\[ \text{Total cost} = 80.5 \, \text{sq. meters} \times 175 \, \text{Rs/sq. meter} \][/tex]
[tex]\[ \text{Total cost} = 14087.5 \, \text{Rs} \][/tex]
### Summary
(a) The correct formula to calculate the area of four walls is:
[tex]\[ (C) \, 2h(\ell + b) \][/tex]
(b) The height of the room is:
[tex]\[ 4 \, \text{meters} \][/tex]
(c) The total cost of painting the walls, excluding the door and windows, is:
[tex]\[ \text{Rs} \, 14087.5 \][/tex]
This completes the solution.
