Answer:
1. For determining the height of the free surface of water in the conical tank:
- a) Apply cone volume formula. The height of the water in the conical tank is approximately 0.008 mm.
2. For determining additional water required to fill the tank:
- a) Find the difference in volumes. The additional volume required to fill the tank is negligible, as the initial volume poured (2 liters) is significantly smaller than the tank's volume.
3. For determining the density of 30.5kg of salad oil:
- d) Salad oil density is not given. Correct, we can't calculate the density of the salad oil without the necessary information.
Step-by-step explanation:
1. To determine the height of the free surface if 2 liters of water is poured into a conical tank with a base diameter of 400mm and a height of 600mm, we can use the cone volume formula.
a) Apply cone volume formula:
The volume of a cone is given by the formula V = (1/3) * π * r^2 * h, where V is the volume, π is a constant (approximately 3.14), r is the radius of the base, and h is the height.
First, we need to convert the volume of water from liters to milliliters, since the dimensions of the tank are given in millimeters. 1 liter is equal to 1000 milliliters, so 2 liters would be 2000 milliliters.
Next, we can substitute the given values into the formula:
V = (1/3) * 3.14 * (200^2) * h
Since the diameter of the base is given as 400mm, the radius would be half of that, which is 200mm.
Simplifying the equation:
2000 = (1/3) * 3.14 * 40000 * h
Solving for h:
h = 2000 / ((1/3) * 3.14 * 40000)
Calculating the value:
h ≈ 0.008 mm
Therefore, the height of the free surface of the water in the conical tank is approximately 0.008 mm.
2. To determine how much additional water would be required to fill the tank, we can use the difference in volumes.
a) Find the difference in volumes:
The initial volume of water poured into the tank is 2 liters, which is equivalent to 2000 milliliters. We have already calculated the volume of the tank to be approximately 0.008 mm^3.
To find the additional volume needed to fill the tank, we can subtract the initial volume from the total volume of the tank:
Additional volume = Total volume - Initial volume
Calculating the additional volume:
Additional volume ≈ 0.008 - 2000
Since the volume of the tank is significantly larger than the initial volume of water poured, the additional volume required to fill the tank is negligible.
3. If the tank was to hold 30.5kg of salad oil, we can calculate the density of the salad oil.
a) Calculate density using mass and volume:
Density is defined as mass per unit volume. In this case, the mass of the salad oil is given as 30.5kg. To calculate the density, we need to know the volume of the salad oil.
b) Use the density formula for water:
Since the density of the salad oil is not given, we cannot directly use the density formula for water. Each substance has its own unique density value.
c) Density remains constant:
The statement "density remains constant" is not applicable in this scenario, as we do not have the density value for the salad oil.
d) Salad oil density is not given:
Indeed, the density of the salad oil is not provided, so we cannot calculate it without this information. The density of a substance is a characteristic property and varies depending on the specific substance.