Let's solve each part of the question step by step.
(i) The total volume of the mixture
The total volume of a mixture is the sum of the volumes of all the components of the mixture. In this case, we have water and milk. The volume of the water is 200 cm³, and the volume of the milk is 300 cm³.
Total volume of the mixture = volume of water + volume of milk
Total volume = 200 cm³ + 300 cm³
Total volume = 500 cm³
So the total volume of the mixture is 500 cm³.
(ii) The total mass of the mixture
To find the total mass of the mixture, we need to calculate the mass of each component and then add them together. The mass of a substance can be found by multiplying its volume with its density.
Mass of water = volume of water × density of water
Mass of water = 200 cm³ × 1 g/cm³
Mass of water = 200 g
Mass of milk = volume of milk × density of milk
Mass of milk = 300 cm³ × 2 g/cm³
Mass of milk = 600 g
Total mass of the mixture = mass of water + mass of milk
Total mass = 200 g + 600 g
Total mass = 800 g
So the total mass of the mixture is 800 grams.
(iii) The density of the mixture in SI units (kg/m³)
Density is defined as the mass per unit volume. To find the density of the mixture in SI units, we will need to express both the mass in kilograms (kg) and the volume in cubic meters (m³).
First, we need to convert the mass from grams to kilograms:
1 kg = 1000 g
Total mass = 800 g ÷ 1000 g/kg
Total mass = 0.8 kg
Next, we convert the volume from cubic centimeters to cubic meters:
1 m³ = 1,000,000 cm³ (since 1 m = 100 cm)
Total volume = 500 cm³ ÷ 1,000,000 cm³/m³
Total volume = 0.0005 m³
Now, we can calculate the density of the mixture:
Density = mass/volume
Density = 0.8 kg / 0.0005 m³
Density = 1600 kg/m³
So the density of the mixture is 1600 kg/m³.
