Question

The base of a rectangular container is a square of side 12 cm. This container 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 224 cm³ of water overflows. Find the volume and surface area of the cube.

Answer 1

When the cube is submerged, the level of water is increased and some water flows out of it.
Volume of the cube
= Volume of water level rise + Volume of water overflown
= 12 x 12 x 2 + 224
= 512cm³
∴  The volume of the cube is 512cm³.  ...(Ans 1)
Volume of the cube
= s³
512 = s³
s = `root(3)(512)`
s = 8cm
Surface area of cube
= 6s²
= 6 x 8²
= 384cm²
∴ The surface area of the cube is 384cm².  ...(Ans2)