To solve this question, we need to find the density of the combined liquid $C$, which results from mixing liquids $A$ and $B$.

Step 1: Determine the volume of liquid A

We are given:

• Density of liquid $A$ ($\rho_A$) = 70 kg/m³
• Mass of liquid $A$ ($m_A$) = 1400 kg

Using the formula: $\text{Density} = \frac{\text{Mass}}{\text{Volume}} \quad \Rightarrow \quad V_A = \frac{m_A}{\rho_A}$

Substitute the values: $V_A = \frac{1400}{70} = 20 \, \text{m}^3$

Step 2: Determine the mass of liquid B

We are given:

• Density of liquid $B$ ($\rho_B$) = 280 kg/m³
• Volume of liquid $B$ ($V_B$) = 30 m³

Using the density formula again, the mass of liquid $B$ is: $m_B = \rho_B \times V_B = 280 \times 30 = 8400 \, \text{kg}$

Step 3: Find the total mass and total volume

• Total mass of liquid $C$ = $m_A + m_B = 1400 + 8400 = 9800 \, \text{kg}$
• Total volume of liquid $C$ = $V_A + V_B = 20 + 30 = 50 \, \text{m}^3$

Step 4: Calculate the density of liquid C

The density of liquid $C$ is given by: $\text{Density of C} = \frac{\text{Total mass of C}}{\text{Total volume of C}} = \frac{9800}{50} = 196 \, \text{kg/m}^3$

Final Answer:

The density of liquid $C$ is 196 kg/m³.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How does changing the volume of liquid B affect the density of liquid C?
2. What if liquid A had a different mass but the same density?
3. How would you solve this problem if both liquids had the same density?
4. Can the density of liquid C ever be lower than the densities of both A and B?
5. How would adding a third liquid affect the overall density?

Tip: When combining liquids, the total mass and total volume both play a crucial role in determining the resulting density. Always calculate them separately before combining.