An object will float at the surface of a liquid if the mass of the object is less than the mass of the liquid that it displaces. A spherical vessel (diameter = 2.00 cm)when empty has a mass of 2.00 g. What is the greatest volume of water that can be placed in the vessel and still have the vessel float at the surface of water? (Given: density of water = 1.00 g/cm³) A)2.00 mL B)31.5 mL C)2.19 mL D)4.19 mL E)the vessel will not float even when empty

Question

Quizplus · Accepted Answer

The volume of the water that can be placed in the vessel without sinking it will be equal to the volume of the displaced water. Let the volume of water that can be filled in the vessel be V. The mass of the empty spherical vessel is 2.00 g. Let the mass of the vessel when it is filled with water be M grams. Therefore, the mass of the water displaced by the vessel will be equal to (M - 2.00) g.

The volume of water displaced can be calculated as follows:

Mass of the water displaced = (M - 2.00) g 
Density of water = 1.00 g/cm³ 
Volume of water displaced = (M - 2.00) g ÷ 1.00 g/cm³ = (M - 2.00) cm³

The volume of water displaced must be equal to the volume of the vessel:

Volume of water displaced = Volume of vessel

4/3πr³  = V

r = d/2 = 1 cm

4/3π1³ = 4.19 cm³

Therefore, V = 4.19 cm³ = 4.19 mL.

The greatest volume of water that can be placed in the vessel and still have the vessel float at the surface of water is 2.19 mL (option C).

An Object Will Float at the Surface of a Liquid