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 m square is rs. 80. find their volumes.
Answers
Answered by
7
Cuboid sides x,2x,4x
Cube side is a
Volume of cube = volume of cuboid
a^3=8x^3
a=2x
Surface area of cube is 6a^2
6×(2x)^2=24x^2
5rs per square so cube charge is
24×5x^2=120x^2
Surface area of cuboid is 2(lb+bh+lh)
2(x×2x + x×4x + 2x×4x)=28x^2
5rs per square so cuboid charge is
28×5x^2=140x^2
Now, 140x^2 - 120x^2=80
20x^2=80
x=2
Volume will be 8x^3=64 is the answer
I think this descriptive solution will help....
Cube side is a
Volume of cube = volume of cuboid
a^3=8x^3
a=2x
Surface area of cube is 6a^2
6×(2x)^2=24x^2
5rs per square so cube charge is
24×5x^2=120x^2
Surface area of cuboid is 2(lb+bh+lh)
2(x×2x + x×4x + 2x×4x)=28x^2
5rs per square so cuboid charge is
28×5x^2=140x^2
Now, 140x^2 - 120x^2=80
20x^2=80
x=2
Volume will be 8x^3=64 is the answer
I think this descriptive solution will help....
Similar questions