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

Expert Answer:

Dear Student,

Since, the length, breadth and height of the cuboid are in the ratio 1:2:4 so let the dimensions of the cuboid be k x 2k x 4k respectively.

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

Regards
Team Topperlearning

Answered by  | 7th Mar, 2011, 02:07: PM

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