Question

Mercury has a density of 13.56 g/mL. How many kilograms of mercury would you expect to fit in a cylindrical glass cup with a bottom radius of 5.75 inches and a height of 0.950 ft?

Answer 1

263.152kg

Step-by-step explanation:

The density of a substance is related to its mass and volume as follows;

density = mass / volume

mass = density x volume -------------(i)

The substance in question here is mercury which has;

density = 13.56g/mL = 13.56g/cm³

Since the mercury is going to be put in the cylindrical glass, the volume of the cylindrical glass is going to be equal to the volume of the mercury that will be put.

And we know that the;

volume of a cylinder = πr²h

Where;

π = 3.142

r = bottom radius of the cylinder = 5.75inches

h = height of the cylinder = 0.950ft

For uniformity, let's convert the radius and height of the cylinder to their corresponding values in cm

r = 5.75 inches = 5.75 x 2.54 cm = 14.605cm

h = 0.950 ft = 0.950 x 30.48 cm = 28.956cm

Therefore, the volume of the cylinder;

v = 3.142 x (14.605cm)² x 28.956cm = 19406.5cm³

v = 19406.5cm³ [This is also the volume of the mercury necessary to fit the cylinder]

Now the following value has been found;

volume = 19406.5cm³

Substitute the values of density and volume into equation (i) as follows;

mass = 19406.5cm³ x 13.56g/cm³

mass = 263152.14g

Convert the result to kg by dividing by 1000

mass = 263.152kg

Therefore, 263.152kg kilograms of mercury would fit in the cylindrical glass.