The density of liquid mercury is 13.5 g/cm cube. What mass of mercury (in kg) is required to fill a hollow cylinder having an inner diameter of 2.00 cm to height of 25.0 cm?
Calculate the volume of the cylinder.
(pi)r^2h
3.142 x 1.0 cm^2 x 25.0 cm = approx 75 cm^3
(but calcutae the exact value)
mass = volume x density
mass = 75 cm^3 x 13.5 g cm^3 = approx 1000 g
(but calcutae the exact value)
or approximately 1 kg
To find the mass of mercury required to fill the hollow cylinder, we need to first calculate the volume of the cylinder and then use the density to determine the mass.
Step 1: Calculate the volume of the cylinder.
The volume of a hollow cylinder can be calculated by subtracting the volume of the inner cylinder from the volume of the outer cylinder.
Volume of outer cylinder = πr^2h
Volume of inner cylinder = πR^2h
Given:
Inner diameter (d) = 2.00 cm
Height (h) = 25.0 cm
The inner radius (r) can be calculated by dividing the inner diameter by 2.
r = d/2 = 2.00 cm/2 = 1.00 cm
The outer radius (R) is equal to the inner radius plus the thickness of the cylinder. However, the thickness is not mentioned in the question. Therefore, we will assume that the thickness is uniform and the same all around.
Let's assume the thickness (t) is 'x' cm.
The outer radius (R) can be calculated by adding the inner radius and the thickness.
R = r + t = 1.00 cm + x cm = 1.00 cm + x cm
So, the volume of the hollow cylinder is calculated as:
Volume = Volume of outer cylinder - Volume of inner cylinder
Volume = πR^2h - πr^2h
Volume = π(1.00 cm + x cm)^2 * 25.0 cm
Step 2: Convert the volume to cubic meters.
Since the density is given in grams per cubic centimeter (g/cm^3) and mass is typically measured in kilograms (kg), we should convert the volume to cubic meters (m^3) in order to get mass in kilograms.
1 m = 100 cm, and 1 m^3 = (100 cm)^3 = 1,000,000 cm^3
Therefore, the volume in cubic meters is:
Volume (m^3) = Volume (cm^3)/1,000,000
Step 3: Calculate the mass using the density.
The mass (m) can be calculated by multiplying the volume by the density.
Mass (kg) = Volume (m^3) * Density (g/cm^3) * 1000 (to convert g to kg)
Let's calculate the mass:
Volume (m^3) = (π(1.00 cm + x cm)^2 * 25.0 cm) / 1,000,000
Density (g/cm^3) = 13.5 g/cm^3
Mass (kg) = Volume (m^3) * Density (g/cm^3) * 1000
Please note that the value of 'x' is required to get accurate results. If you have the thickness, you can substitute it into the calculations to find the precise mass.
To find the mass of mercury required to fill the hollow cylinder, we need to calculate the volume of the cylinder and then multiply it by the density of mercury.
Step 1: Calculate the volume of the cylinder.
The volume of a cylinder can be calculated using the formula: V = πr^2h, where r is the radius and h is the height.
Given that the inner diameter is 2.00 cm, we can find the radius by dividing it by 2. So, the radius (r) = 2.00 cm / 2 = 1.00 cm = 0.01 m (converting cm to m).
Using the given height of 25.0 cm, the volume of the cylinder (V) is:
V = π(0.01 m)^2 * 25.0 cm = π(0.01 m)^2 * 0.25 m = π * 0.0001 m^3 * 0.25 m = 0.00007854 m^3.
Step 2: Multiply the volume by the density to find the mass.
We are given that the density of liquid mercury is 13.5 g/cm^3. To convert this to kg/m^3, we need to divide it by 1000. So, the density of mercury in kg/m^3 is 13.5 g/cm^3 / 1000 = 0.0135 kg/cm^3.
Now, we can find the mass (m) of the mercury by multiplying the volume of the cylinder by the density:
m = V * density = 0.00007854 m^3 * 0.0135 kg/cm^3.
Finally, we need to convert the mass from kg/cm^3 to kg. Since 1 cm^3 = 0.000001 m^3, we can simplify the formula to:
m = 0.00007854 m^3 * 0.0135 kg/cm^3 * (1 cm^3 / 0.000001 m^3) = 78.54 kg * 0.0135.
Therefore, the mass of mercury required to fill the hollow cylinder is approximately 1.060 kg.