Question

The length of a room is 5m, breadth is 3.5m and height is 4m. Find the total expenditure of whitewashing on the four walls and roof at the rate of 15 per square meter. (Answer correctly up to 1 decimal place)

Answer 1

Hint: We use the formula of surface area of cuboid to calculate total surface area and subtract the surface area of the floor from total surface area. Use a unitary method to calculate the total cost of white washing the obtained area.
* Surface area of a cuboid having length \[l\], breadth \[b\] and height \[h\] is \[2(lb + bh + hl)\]
* Unitary method helps us to calculate the value of multiple units by multiplying value of single unit to number of units given

Complete step by step solution:
Write the dimensions of room
Since, length \[ = 5\]m
\[ \Rightarrow l = 5\]
Since, breadth \[ = 3.5\]m
\[ \Rightarrow b = 3.5\]
Since, height \[ = 4\]m
\[ \Rightarrow h = 4\]
\[\therefore l = 5,b = 3.5,h = 4\].....................… (1)
Now we write the formula of surface area of walls and floor of the room

Let the total surface area of the cuboidal room be \[S\]
Then we can write the formula of total surface area of room as \[S = 2(lb + bh + hl)\]
Since we have to find the surface area of four walls and roof of the room, we subtract the area of the floor. Let the surface area of four walls and roof of the room be denoted by \[C\].
Area of floor of the room \[ = l \times b\]
\[ \Rightarrow \]Surface area of four walls and roof of the room \[ = S - \left\{ {(l \times b)} \right\}\]
\[ \Rightarrow C = 2(lb + bh + hl) - lb\]
\[ \Rightarrow C = 2lb + 2bh + 2hl - lb\]
Calculate the value in RHS
\[ \Rightarrow C = lb + 2bh + 2hl\]..................… (2)
Calculate the area to be white washed
Substitute the values of \[l,b,h\] from equation (1) in equation (2)
\[ \Rightarrow \]Area of walls to be white washed \[ = \left( {5 \times 3.5 + 2(3.5 \times 4) + 2(4 \times 5)} \right){m^2}\]
\[ \Rightarrow \]Area of walls to be white washed \[ = \left\{ {17.5 + 28 + 40} \right\}{m^2}\]
Add the terms within the bracket
\[ \Rightarrow \]Area of walls to be white washed \[ = 85.5{m^2}\]..................… (3)
Now we calculate the cost of white washing the total area obtained
Use a unitary method to calculate the cost of white washing the walls and roof by multiplying the total surface area of walls and walls by cost of white washing per unit square meter.
Cost of white washing 1 sq.m of room \[ = Rs15\]
\[ \Rightarrow \]Cost of white washing 85.5 sq.m of room \[ = Rs(85.5 \times 15)\]
\[ \Rightarrow \]Cost of white washing 85.5 sq.m of room \[ = Rs1282.5\]

\[\therefore \]Cost of white washing four walls and roof of the room is Rs.1282.5

Note: Many students make mistakes in calculating the area of four walls and roof as they get confused about what area to subtract from total area, keep in mind the measurements length and breadth make up the floor of the room so we subtract area formed by measurements length and breadth. Also, keep in mind to write units along with the final answer.