Question

A cube and cuboid have same volume. The dimensions of the cuboid are in the ratio 1:2:4. if the difference betweenthe cost of polishing the cube and cuboid at the rate of $5 per m^2 is $80, find their volumes.

Answer 1

Say side of cube = x
Let sides of cubiod = y, 2y & 4y

so, Volume of Cube = Volume of Cubiod
$x^3=8y^3$
x=2y

As the equation surface area of cube =4x^2                                                
                                                      =4 X (2y)^2                                          
                                                      =16y^2

Similarly surface area of cubiod =2h(l+b)                                                      
                                               = 2 X 4y(1y+2y)                                          
                                               =24y^2

Cost of polishing the cube and cuboid at the rate of $5 per m^2

so,
5(24y^2-16y^2)=80 
By solving we get,
=>24y^2-16y^2=18
8y^2=18
y^2=18/8
y=3/2=1.5m
Side of Cube is =2y=3m

As both have same volume, so the volume is $=27m^3$