Question

A square-based rectangular aquarium is filled with water. The side length of the base is 40 cm. The height of the aquarium is 50 cm. The height of the water is

equal to half the height of the aquarium. A solid cube with side length 20 cm is
then thrown into the aquarium and sinks to the bottom.

Does the water level now reach the top of the tank? If not, how far below the top
of the tank does the water reach?

Answer 1

Length & breadth of the aquarium = 40cm(as it is square)

Volume of aquarium = l x b x h

volume of aquarium = 40 x 40 x 50 = 80000 cm³

Volume of water = ½ half of aquarium

Volume of water = ½ x 80000 = 40000 cm³

Volume of the solid cube = a³ = (20cm)³ = 8000cm³

Surely, 40000>>>8000, level doesnt reach the top of the tank.

Volume ocquired = 40000+8000=48000 cm³

Now, let it has reached reached a height h from the ground(bottom).

Volume = 48000 => lx b x h = 48000

=> 40 x 40 x h = 48000

=> h = 30 cm

The height at which water has reached is 30 cm(from bottom).

Thus, below the top it has reached = total height - 30 cm = 50 - 30 = 20 cm