`A` solid cube, with faces either vertical or horizontal, is floating in a liquid of density `6g//c c`. It has two third of its volume submerged. If enough water is added from the top so as to completely cover the cube, what fraction of its volume will remain immersed in the liquid?

Answer

`3//5`

Explanation

weight = buoyancy
`W=B_(l)`
`Vrhog=(2)/(3)Vrho_(l)g`
`rho=(2)/(3)xx6g//c c implies rho=4g//c c`
`W=B_(l)+B_(w)`
`a^(3)rhog=a^(2)xrho_(l)g+a^(2)(a-x)rho_(w)g implies arho=xrho_(l)+(a-x)l_(w)`
`axx4=x xx 6+(a-x)xx1" " implies 4a=6x+a-x`
`x=(3)/(5)a`
`V=a^(2)x " "=V=(3)/(5)a^(3)" "V=(3)/(5)V`