Let's break down the tasks and problems visible in the image:

1. Problem 31: Calculate the density of the box using the 5-step method.

   • The dimensions of the box are provided: 10 cm x 5 cm x 2 cm, with a mass of 300 grams.

   To calculate the density, we can follow these steps:

   • Step 1: Calculate the volume of the box using the formula for volume: $V = \text{length} \times \text{width} \times \text{height}$ In this case: $V = 10 \, \text{cm} \times 5 \, \text{cm} \times 2 \, \text{cm} = 100 \, \text{cm}^3$

   • Step 2: Use the density formula: $\rho = \frac{m}{V}$ Where:

     • $m$ is the mass of the box (300 grams).
     • $V$ is the volume (100 cm³).

     Substituting: $\rho = \frac{300 \, \text{g}}{100 \, \text{cm}^3} = 3 \, \text{g/cm}^3$

   Answer for Problem 31: The density of the box is 3 g/cm³.

2. Problem 32: Calculate the density of the 30g rock using the 5-step method.

   • The rock causes a displacement in the graduated cylinder from 30 mL to 40 mL. This means the volume of the rock is: $V_{\text{rock}} = 40 \, \text{mL} - 30 \, \text{mL} = 10 \, \text{mL} = 10 \, \text{cm}^3$
   • The mass of the rock is given as 30 grams.

   Using the density formula: $\rho = \frac{m}{V} = \frac{30 \, \text{g}}{10 \, \text{cm}^3} = 3 \, \text{g/cm}^3$

   Answer for Problem 32: The density of the rock is 3 g/cm³.

3. Problem 33: Solve for the variable $b$ in the equation: $a = \frac{b}{c \cdot 9}$ To solve for $b$, multiply both sides of the equation by $c \cdot 9$: $b = a \cdot c \cdot 9$

Would you like further details or have any questions?

Here are some related questions:

1. How would you calculate density if the object is irregularly shaped?
2. Can you derive a formula to calculate density in different units?
3. What is the significance of density in practical applications like buoyancy?
4. How can we use the water displacement method to find the volume of an irregular object?
5. Can the density of an object change with temperature or pressure?

Tip: When using the water displacement method to find volume, remember that 1 mL of water equals 1 cm³ in volume.