A cube and cuboid have same volume. The dimensions of the cuboid are in the ratio 1:2:4. If the difference between cost of polishing cube and cuboid at the rate of Rs.5 per metre square is Rs. 80 .Find their volumes.
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let common ratio be x. so, dimensions = x,2x,4x
cuboid volume = x (2x)(4x) =8x³
so, cube volume = 8x³
side of cube = ³√8x³ = 2x
surface area of cube = 6(2x)= 24x²
cost =24x²*5 =120x²
surface area of cuboid =2(2x*x+4x*x+2x*4x)
= 28x²
cost = 28x²*5 =140x²
140x²-120x² =20x²
20x² =Rs. 80
x² =80/20 =4
x= 2 metres.
their volumes = 4*4*4 = 2(4+9+16)
64 =2(32) = 64 m²
cuboid volume = x (2x)(4x) =8x³
so, cube volume = 8x³
side of cube = ³√8x³ = 2x
surface area of cube = 6(2x)= 24x²
cost =24x²*5 =120x²
surface area of cuboid =2(2x*x+4x*x+2x*4x)
= 28x²
cost = 28x²*5 =140x²
140x²-120x² =20x²
20x² =Rs. 80
x² =80/20 =4
x= 2 metres.
their volumes = 4*4*4 = 2(4+9+16)
64 =2(32) = 64 m²
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