28.A cube and a cuboid have the same volume. The dimensions of the cuboid are in the ratio 1 : 2 : 4. If the difference between the cost of painting the cuboid and cube (whole surface area) at the rate of Rs 5 / m2 is Rs 80. Find their volumes.
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Volume of cube=volume of cuboid
a3=l•b•h
a3=x•2x•4x
a3=8x3
a=3√8x
a=2x
Surface area of cube=6a2
=6•2x2
=6•4
=24x2
Surface area of cuboid=2[l•b+b•h+h•l]
=2[2x^2+8x^2+4x^2]
=2[14x^2]
=28x^2
Cost of painting of cuboid - cost of painting of cube=80
=28x^2•5-24x^2•5
=140x^2-120x^2
=20x^2=80
x^2=80÷20
x^2=4
x=2
Volume of cube = a^3
=2x^3
=2•2^3
=4^3
=64cm^3
a3=l•b•h
a3=x•2x•4x
a3=8x3
a=3√8x
a=2x
Surface area of cube=6a2
=6•2x2
=6•4
=24x2
Surface area of cuboid=2[l•b+b•h+h•l]
=2[2x^2+8x^2+4x^2]
=2[14x^2]
=28x^2
Cost of painting of cuboid - cost of painting of cube=80
=28x^2•5-24x^2•5
=140x^2-120x^2
=20x^2=80
x^2=80÷20
x^2=4
x=2
Volume of cube = a^3
=2x^3
=2•2^3
=4^3
=64cm^3
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