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

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