Question

A rectangular box, whose base is a square of side 5 cm, stand on a horizontal table and holds water up to 2 cm from the top. When a cube is placed in the water and is completely submerged, the water rises to the top and 14 cube cm of water overflows. Calculate the volume of the cube. Also find its total surface area.

Answer 1

Volume of cube= Volume of the water displaced.
Volume of water displaced= $2\times 5\times 5+14c{m}^3$
$=50+14=64c{m}^3$
Thus volume of cube = volume of water displaced= 64
Volume of a cube $=a^3$ (Where a is the side of the cube)
Thus, a= cube root of 64= 4cm
Surface area of the cube $=6a^2=6\times 16=96c{m}^2$