Question

The dimensions of room are in the ratio 3:2:1.its total surface area is 550m.find the cost of white washing walls and ceiling of the room at rs 20 per m.

Answer 1

T.S.A of room = 2(lb+bh+hl)
Let length of room be 3x
Let breadth of room be 2x
and height of room be x
T.S.A=550m
2(lb+bh+hl) = 550
2[(3x)(2x)+(2x)(x)+(x)(3x) = 550
2(6x square)+(2x square)+(3x square) =550
2×11x square =550
22x square = 550
x square = 550÷22
x square = 25
so x = 5
Therefore, length = 3x = 3×5 = 15m
breadth =2x =2×5 = 10m
height = x = 5m
Now,C.S.A = 2(lh+hb)
= 2[(15)(5)+(5)(10)]
= 2(75)+(50)
= 2(125)
= 250m square
Area of Ceiling wall = l×b
= 15×10 =150m square
Total area = 250+150 = 400m square
Cost of white washing at 1m per square = 20rs
Cost of white washing at 400m per square= 400×20 = 8000Rs