gasoline and water are immiscible. Regular-grade gasoline has a lower density than water. A 100mL graduated cylinder with an inside diameter of 3.2 cm contains 34 g of gasoline and 34 g of water. What is the combined height of the two liquid layers in the cylinder? The volume of a cylinder is pi radius squared X h, h is the height.
start with volume = mass/density
find the density of each liquid, and you can figure the volume.
Then volume = arae * height
You know the area of the liquid cross-section, so once you know the total volume, the height is
height = volume/area
To find the combined height of the two liquid layers in the cylinder, we need to determine the volumes of gasoline and water separately.
First, let's find the volume of gasoline:
Given that the density of gasoline is lower than water, we know that the mass of gasoline will occupy a larger volume than the mass of water. We also have the mass of gasoline, which is 34 g. We can calculate the volume for gasoline by dividing the mass by its density.
Density of gasoline is not given in the question, but for the purpose of this explanation, let's assume it is 0.72 g/mL (typical value for gasoline).
Therefore,
Volume of gasoline = mass of gasoline / density of gasoline
Volume of gasoline = 34 g / 0.72 g/mL
Volume of gasoline ≈ 47.2 mL
Next, let's find the volume of water:
Similarly, we have the given mass of water, which is also 34 g. To calculate the volume of water, we need to divide the mass by its density.
Density of water = 1 g/mL (typical value for water)
Therefore,
Volume of water = mass of water / density of water
Volume of water = 34 g / 1 g/mL
Volume of water = 34 mL
Now we know the volumes of gasoline and water.
To find the combined height of the two liquid layers, we can add the heights of gasoline and water.
Given the formula for the volume of a cylinder:
Volume of cylinder = π × radius² × height
We can rearrange the formula to solve for height:
Height = Volume of cylinder / (π × radius²)
The given cylinder has an inside diameter of 3.2 cm, which means the radius is half of that. So, the radius would be 1.6 cm or 0.016 meters as it's more commonly used in calculations.
Now, let's calculate the combined height of the two liquid layers in the cylinder using the formula:
Height = (Volume of gasoline + Volume of water) / (π × radius²)
Height = (47.2 mL + 34 mL) / (π × (0.016 m)²)
Height = 81.2 mL / (π × 0.000256 m²)
Height ≈ 81.2 mL / 0.00080384 m²
Height ≈ 101,011 mL/m²
So, the combined height of the two liquid layers in the cylinder is approximately 101,011 mL/m².