A rectangular container, whose base is a square of side 5 cm, stands on a horizontal table, and holds water upto 1 cm from the top. When a cube is placed in the water it is completely submerged, the water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also the length of its edge.
Base of the container = 5 cm×5 cm
After placing a cube in it, the water rises to the top (i.e. by 1 cm) and 2 cubic cm of water overflows.
(i) ∴ Volume of water = 5×5×1+2=25+2=27 cm3
∴ Volume of cube = 27 cm3
(ii) Then edge of the cube = 3√27=3 cm