# 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 = 6x3

Let edge of the cube = a

Thus, volume of the cube = a3

Since, volume of cube and cuboid is same. Therefore, Surface area of the cube = 6a2 = 6(2x)2 = 24x2

So, cost of polishing the cube @ 5/m2 = Rs (24x2×5) = Rs 120x2

And, surface area of the cuboid So, cost of polishing the cuboid @ 5/m2 = Rs (28x2×5) = Rs 140x2

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 = a3 = (4)3 = 64 m3

Thus, volume of the cuboid = volume of the cube = 64 m3

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

given,

Volume of cuboid=volume of cube

x*2x*4x=a3

8x3=a3

or a=2x

Cost of polishing the cuboid at rs.5/m2=T.S.A. of cuboid*5

=2(x*2x+2x*4x+4x*x)*5=140x2

Cost of polishing the cube at rs.5/m2=T.S.A. of cube*5

= 6a2*5

or 6*(2x)2*5=120x2

Given 140x2-120x2=80

or 20x2=80 or x=2m

Therefore Volume of cuboid= Volume of cube= x*2x*4x=2*4*8=64m3

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