The length,breadth,height,of a room are 6m,4.5m,3m. find the cost of whitewashing the walls of the room and the ceiling at the rate of 8 per meter square.
Answers
Area to be whitewashed = area of four walls + area of ceiling
Formulas to be noted : -
Area of four walls = 2( length + breadth ) x height
Area of ceiling = area of rectangle = length x breadth
In the question, length of the room = 6 m
breadth of the room = 4.5 m
height of the room = 3 m
On the basis of formulas given above : -
Area of four walls = 2( 6 m + 4.5 m ) x 3 m
Area of four walls = 2( 10.5 m ) x 3 m
Area of four walls = 21 m x 3 m
Area of four walls = 63 m^2
Area of ceiling = 6 m x 4.5 m
Area of ceiling = 27 m^2
Therefore, area to be whitewashed = 63 m^2 + 27 m^2
Area to be whitewashed = 90 m^2
Cost of whitewashing = rate at which area is being whitewashed x area to be whitewashed
Cost of whitewashing = Rs 8 / m^2 x 90 m^2
Cost of whitewashing = Rs 8 x 90
Cost of whitewashing = Rs 720.
Given Dimensions are:
⇒ Length of the room = 6m.
⇒ Breadth of the room = 4.5m.
⇒ Height of the room = 3m.
Now,
(i)
Area of cuboid = 2(lb + bh + lh)
⇒ 2(6 * 4.5 + 4.5 * 3 + 6 * 3)
⇒ 2(58.5)
⇒ 117.
(ii)
Area of base = length * breadth
= 6 * 4.5
= 27.
(iii)
Area to be white-washed = Area of cuboid - Area of base
= 117 - 27
= 90 m^2.
Given that cost of white-washing per m^2 = 8.
Then the cost of 90 m^2 = 90 * 8
= 720 .
Therefore, cost of white-washing the walls of the room = 720.
Hope it helps!