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CBSE Class 9 Answered

A cube and cuboid have same volume. The dimensions of the 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 per m2 is Rs. 80, find their volumes.
Asked by Topperlearning User | 10 Oct, 2014, 02:11: PM
answered-by-expert Expert Answer

Let the dimensions of cuboid be x, 2x, 4x

Volume of cuboid = 8x3

Volume of cube = 8x3 = side3

So, side of cube = 2x

TSA of cuboid = 2(lb + bh + hl) = 2(2x2 + 8x2 + 4x2) = 28x2

Cost of polishing the cuboid = Rs. 5 28 x2 = 140x2

TSA of cube = 6(side)2 = 6(2x)2 = 24x2

Cost of polishing the cube = Rs. 5 24 x2 = 120x2

Now, from the given information, we have

140x2 - 120x2 = 80

20x2 = 80

x2 = 4

x = 2

Volume of cuboid = Volume of cube = 8 (2)3 cubic cm= 64 cubic m

Answered by | 10 Oct, 2014, 04:11: PM

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