Question

A class room is 12m long, 10m wide and 4.5m high. Find the cost of white washing its walls and ceiling at the rate of Rs. 8 per $ {m^2} $ .

Answer 1

Hint: Find the total surface area of the classroom using the formula total surface area of a cuboid as a classroom with length, height and width will be in the form of a cuboid. Total surface area includes the area of all the walls, ceiling and floor. So subtract the area of the floor from it. Multiply this resulting area with Rs. 8 to get the total cost of white washing the ceiling and walls of the classroom.
Total surface area of a cuboid is $ 2\left( {lw + wh + lh} \right) $ , where l is the length, w is the width and h is the height of the cuboid.
Area of a rectangle is $ l \times w $ , where l is the length and w is the width (breadth) of the rectangle.

Complete step-by-step answer:
We are given that a class room is 12m long, 10m wide and 4.5m high and the cost of white washing its walls and ceiling is Rs. 8 per $ {m^2} $ .
We have to find the total cost of white washing its ceiling and walls.
 

Total surface area of the classroom is $ 2\left( {lw + wh + lh} \right) $ , where length is 12m, width is 10m and height is 4.5m.
 $
  TS{A_{classroom}} = 2\left( {lw + wh + lh} \right) \\
  l = 12m,w = 10m,h = 4.5m \\
   \Rightarrow TS{A_{classroom}} = 2\left( {12 \times 10 + 10 \times 4.5 + 12 \times 4.5} \right) \\
   \Rightarrow TS{A_{classroom}} = 2\left( {120 + 45 + 54} \right) \\
   \Rightarrow TS{A_{classroom}} = 2 \times 219 \\
  \therefore TS{A_{classroom}} = 438{m^2} \\
 $
Area of the floor is $ l \times w = 12 \times 10 = 120{m^2} $
The total surface area of just the walls and ceiling is $ 438 - 120 = 318{m^2} $
The cost of white washing 1 $ {m^2} $ is Rs. 8.
Then the cost of white washing $ 318{m^2} $ is $ 318 \times 8 = Rs.2554 $
The total cost of white washing the ceiling and walls of the classroom is Rs. 2,554.

Note: A cube also has a length, a width and a height but we have considered the classroom as a cuboid because the length, breadth and height are equal in a cube but not in a cuboid. Here they are not equal so it is in the form of a cuboid. Total surface area is the sum of lateral surface area, area of the top and area of the base. Here we do not require the area of the base (floor) so we subtracted it from the TSA and solved further.