https://file.aiquickdraw.com/mathbot/file/1727272762856k5vyyfuy.jpg

Let's break down the problem to determine whether the brick will sink, using the formula for density provided in the image.

### Given Information:
1. **Dimensions of the brick**: 
   - Length = 22 cm
   - Width = 10 cm
   - Height = 8 cm

2. **Mass of the brick**: 
   - Given mass in pounds = 4.5 lb

3. **Density formula**: 
   \[
   \text{Density} = \frac{\text{mass in grams}}{\text{volume in cm}^3}
   \]
   The brick must have a density **more than 1 g/cm³** for it to sink.

### Steps to solve:

1. **Calculate the volume of the brick**:
   \[
   \text{Volume} = \text{Length} \times \text{Width} \times \text{Height}
   \]
   \[
   \text{Volume} = 22 \, \text{cm} \times 10 \, \text{cm} \times 8 \, \text{cm} = 1760 \, \text{cm}^3
   \]

2. **Convert mass from pounds to kilograms**:
   From the conversion graph, 4.5 pounds is approximately **2 kg**.

3. **Convert kilograms to grams**:
   Since 1 kg = 1000 g,
   \[
   2 \, \text{kg} = 2000 \, \text{g}
   \]

4. **Calculate the density**:
   Using the formula:
   \[
   \text{Density} = \frac{\text{Mass}}{\text{Volume}} = \frac{2000 \, \text{g}}{1760 \, \text{cm}^3} \approx 1.14 \, \text{g/cm}^3
   \]

Since the density of the brick is **1.14 g/cm³**, which is **greater than 1 g/cm³**, the brick will sink.

### Conclusion:
Yes, the brick will sink because its density is 1.14 g/cm³, which is higher than the required 1 g/cm³.

---

Would you like more details or have any questions? 

Here are 5 follow-up questions:
1. How does density affect an object's ability to sink or float?
2. What other units could mass and volume be measured in for density calculations?
3. What role does water's density (1 g/cm³) play in determining whether an object will sink or float?
4. If the brick were lighter, how would its sinking behavior change?
5. How would changing the dimensions of the brick impact its density?

**Tip:** Always check that your units are consistent (e.g., grams and cm³) when calculating density.

Will the brick sink? Explain your answer using figures.

Learn how to calculate the density of a brick and determine if it will sink. This problem covers density, volume, and unit conversion, with step-by-step explanations. Suitable for students in Grades 7-9.

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