It cost Rs. 1089 to paint all the surfaces of a cube at the rate of Rs. 1.5 per meter sq. If the same cube is cut to form three cuboids of equal volumes, then the cost of painting all the surfaces of any two of the cuboids so formed at the 50% more rate is
Surface area of a cube = 6a², where a=side
Cost of painting = Surface Area*Rate per meter sq.
1089 = 6a²*1.5
⇒ a²=121 or a=11
When the cube is cut to form three cuboids of equal volume, one of the edge (side) will be divided into 3 equal parts.
Then, sides of each cuboid are 11/3, 11 and 11 m.
.'. Surface area of a cuboid = 2*[(11/3)*11 + (11/3)*11 + 11*11] = 1210/3
New cost of painting = (150/100)*1.5 = 9/4/m sq.
Hence cost of painting 2 cuboids = 2*(9/4)*(1210/3) = 1815
Correct Option 5)