Question

A solid cube of side 8cm is dropped into a cylindrical tank of radius 7cm.calculate the rise in the water level if the original depth of water was 9cm

Answer 1

The volume of the cube is V1 = (8 cm)^3 = 512 cm^3.

The volume of water displaced by the cube when it is completely submerged is equal to the volume of the cube, which is 512 cm^3.

The formula for the volume of a cylinder is V = πr^2h, where r is the radius and h is the height.

If the original depth of water was 9cm, the initial height of the water in the cylinder is h1 = 9cm.

After the cube is dropped in, the volume of water in the cylinder increases by 512 cm^3. Therefore:

πr^2h2 - πr^2h1 = 512

πr^2(h2 - h1) = 512

h2 - h1 = 512 / (πr^2)

h2 - 9 = 512 / (π(7)^2)

h2 - 9 ≈ 1.45 cm

Therefore, the water level rises by approximately 1.45 cm.