Question

A conical vessel, with base radius 5 cm and height 24 cm, is full of water. Ts water is emptied into a cylindrical vessel of base radius 10 cm. Find the height to wch the water will rise in the cylindrical vessel. [Use π=22/7] OR A sphere of diameter 12 cm, is dropped in a right circular cylindrical vessel, partly filled with water. If the sphere is completely submerged in water, the water level in the cylindrical vessel rises by 5 3 9 cm. Find the diameter of the cylindrical vessel.

Answer 1

Amount of water in conical vessel = 1/3π×5^2×24 = 200π cm3.

Let height of water in cylindrical vessel is h.
π×10^2×h = 200π
h = 2 cm.

Volume of sphere = 4/3π × 12^3 = 2304π cm3.

Let radius of cylindrical vessel is R.
According to Archimedes principle,
Increased volume of water = Volume of sphere.

π×R^2 ×53.9 = 2304π
R = 6.538 cm.
Diameter = 2R = 13.076 cm