Question

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 and is completely submerged, the water rises to the top and 2 cm³ of water overflows. Calculate the volume of the cube and the length of its edge.

Answer 1

Given: Rectangular container with square base side = 5 cm, water is 1 cm below the top; when a cube is completely submerged the water reaches the top and 2 cm³ overflows.

Step-wise calculation:

1. Base area

= 5 cm × 5 cm 

= 25 cm²

2. Water rises by 1 cm to reach the top, so volume displaced by this rise

= Base area × Rise 

= 25 cm² × 1 cm

= 25 cm³

3. Extra overflow volume = 2 cm³.

4. Volume of cube

= Volume causing rise + Overflow

= 25 cm³ + 2 cm³

= 27 cm³

5. Edge length l of cube:

l³ = 27

⇒ `l = root(3)(27)`

⇒ l = 3 cm

Volume of the cube = 27 cm³.

Edge length of the cube = 3 cm.