a cube and cuboid have same volume. dimentions of cuboid are in the ratio 1:2:4. if the difference betwween the cost of polishingthe cube and the cuboid is at the rate of rs5 /m2 is rs 80, find the volumes

**Given that:** The dimension of the cuboid are in the ratio 1:2:4. Let length, breadth and height of the cuboid be l, b and h respectively. So,

l = x, b = 2x and h = 4 x

So, Volume of the cuboid = l×b×h = 6x^{3}

Let edge of the cube = a

Thus, volume of the cube = a^{3}

Since, volume of cube and cuboid is same. Therefore,

Surface area of the cube = 6a^{2} = 6(2x)^{2} = 24x^{2}

So, cost of polishing the cube @ 5/m^{2} = Rs (24x^{2}×5) = Rs 120x^{2}

And, surface area of the cuboid

So, cost of polishing the cuboid @ 5/m^{2} = Rs (28x^{2}×5) = Rs 140x^{2}

Given, the difference between the cost of polishing the cube and cuboid = Rs 80

So,

Thus, Edge of the cube = a = 2x = 2(2) = 4 m

Volume of the cube = a^{3} = (4)^{3} = 64 m^{3}

Thus, volume of the cuboid = volume of the cube = 64 m^{3}

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