Question

the dimensions of a rectangular solid are in the ratio of 1:6:6 and its volume is 562.5 cu. cm. find the volume of a cube whose surface area is equal to the surface area of a rectangular solid

Answer 1

let the dimensions be x,6x,6x,then
x*6x*6x=562.5
x^3=562.5/36=15.625
x=2.5
sides are 2.5,15,15
surface area s=2(l*b+b*h+l*h)
=2(2.5*15+15*15+2.5*15)
=2*15(2.5+15+2.5)
=30*20=600
Let y be the edge of cube ,then
surface area of cube S=6y^2=600
y^2=600/6=100
y=sqrt100=10
volume of cube=10^3=1000 cm^3