A classroom is $7 m$ long, $6 m$ broad and $3.5 m$ high. Doors and windows occupy an area of $17 m 2 .$ What is the cost of white washing the walls at the rate of Rs.1.50 per $m 2$ ?

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answer is C.

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Detailed Solution

It is given a classroom of length 7 m, breadth 6 m and height 3.5 m and the cost of white washing the walls is Rs.1.50 per

m 2

⇒ l = 7

⇒ b = 6

⇒ h = 3.5

m
Let the total surface area of the cuboidal classroom be S.
Then the formula of the total surface area of the classroom is given as S=2(lb+bh+hl). Since, we have to find the surface area of the four walls of the room; we subtract the area of the floor and ceiling of the room.
Let the surface area of four walls of the room be denoted by C.
Area of the floor of the room

= l × b

Similarly, the area of ceiling of the room

= l × b

The surface area of four walls of the room is,

C = S − (l × b) + (l × b)

⇒ C = 2 (l b + b h + h l) − 2 l b

⇒ C = 2 l b + 2 b h + 2 h l − 2 l b

⇒ C = 2 b h + 2 h l

Take 2h common from both terms in RHS.

⇒ C = 2 h (l + b)

… (1)
To calculate the area to be whitewashed, subtract the area of windows and doors from the surface area of the walls of the classroom.
Since, the area covered by doors and windows on the walls is 17