A rectangualr container whose base is a square of side 15 cm stands on a horizointal table and holds water up to 3cm from the top .When a cube is placed in the water and is completely submerged , the water rises to the top and 54 `cm^(3)` of water overflows.
Calculate the volume of the cube and its surface area.

Answer

126800 `cm^(3)`,15880 `cm^(2)`

Explanation

Volume of the cube submerged = volume of water that fills 3cm height of the container +volume of water that overflows
=`15xx15xx3+54=729 cm^(3)`
If side of the cube submerged = x cm
Its volume =`x^(3) cm^(3)`
`x^(3)=729=9xx9xx9xx`
x=9cm
The side of the cube = 9cm
And its surface area =`6xx(side^(2))=6xx9xx9=486 cm^(2)`