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.
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☆☆ranshsangwan☆☆
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
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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