a cube and cuboid have the same volume. the dimensions of cuboid are in the ratio 1:2:4 if the difference between the cost of polishing the cube and cuboid at the rate of Rs.5/m2 is Rs.80. find their volume
Asked by Ranjith Kumar | 7th Mar, 2011, 07:06: PM
Dear Student,
Again, let each edge of the cube be a metres
Now, Vcube = Vcuboid (given)
so, a3 = 8k3
=> a = 2k
Again, t.s.a of the cube = 6 a2 = 6 (2k)2 = 6 x 4 k2 = 24k2
so cost of polishing it @ Rs.5/m2 = 5 x 24k2 = Rs. 120k2
Again, t.s.a of the cuboid = 2(lb + bh + lh) = 2(k.2k + 2k.4k + k.4k) = 2(2k2 + 8k2 + 4k2) = 2(14k2) = 28k2
so cost of polishing it @ Rs.5/m2 = 28k2 x 5 = Rs. 140k2
A to Q
140k2 - 120k2 = 80
=> 20k2 = 80
=> k = 2 => a = 4
Thus, volume of the cube = 64 m3 and
volume of the cuboid = 64 m3
Answered by | 7th Mar, 2011, 02:07: PM
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