what is the mass density of mercury is 13.6g/cm^3. A cylinder of mercury has a diameter of 1 cm and a height of 76cm. what would the height of the cylinder of the water having a diameter of 1 cm and a mass equal to the mass of the mercury cylinder?
The density13.5g/cm3 calculate the mass of 8.20cm3
To find the height of the water cylinder, we can use the concept of mass density. Mass density (ρ) is defined as the mass (m) of a substance per unit volume (V). It is calculated using the formula:
ρ = m/V
We know that the mass density of mercury is 13.6 g/cm^3. We have the diameter (d) of the mercury cylinder as 1 cm and the height (h) as 76 cm.
To find the mass (m) of the mercury cylinder, we can use the formula for the volume (V) of a cylinder:
V = π * (d/2)^2 * h
For the mercury cylinder:
m = ρ * V
Now, to find the height of the water cylinder with the same mass as the mercury cylinder, we need to calculate the volume of the water cylinder.
The formula for the volume of a cylinder is:
V = π * (d/2)^2 * h
We are given that the diameter (d) is 1 cm, but we need to find the height (h) of the water cylinder.
So, let's solve for the height (h) of the water cylinder:
Step 1:
Calculate the volume (V) of the mercury cylinder:
V = π * (1 cm/2)^2 * 76 cm
Step 2:
Calculate the mass (m) of the mercury cylinder:
m = 13.6 g/cm^3 * V
Step 3:
Using the mass (m) of the mercury cylinder, calculate the volume (V) of the water cylinder using the mass density of water (assumed to be 1 g/cm^3):
V = m / 1 g/cm^3
Step 4:
Now, rearrange the formula for the volume of a cylinder to find the height (h) of the water cylinder:
h = V / (π * (1 cm/2)^2)
Step 5:
Substitute the value of V from Step 3 to calculate the height (h) of the water cylinder.
Now, perform the calculations using the given values to find the height of the water cylinder.