SOLUTION: Fdocuments in science 8 density calculations 8 density ... - Free Printable
Educational worksheet: SOLUTION: Fdocuments in science 8 density calculations 8 density .... Download and print for classroom or home learning activities.
PNG
1275×1650
359.9 KB
Free · Personal Use
Quality Assured by Worksheets Library Team
Reviewed for educational accuracy and age-appropriateness
ID: #962739
⭐
Show Answer Key & Explanations
Step-by-step solution for: SOLUTION: Fdocuments in science 8 density calculations 8 density ...
▼
Show Answer Key & Explanations
Step-by-step solution for: SOLUTION: Fdocuments in science 8 density calculations 8 density ...
The image you've uploaded is a completed Density Calculations Worksheet for Science 8, with all problems solved and answers provided. Below is a detailed explanation of each problem and its solution, along with the correctness verification.
---
$$
\text{Density (D)} = \frac{\text{Mass (m)}}{\text{Volume (V)}}
$$
We use this formula in various forms:
- $ D = \frac{m}{V} $
- $ m = D \times V $
- $ V = \frac{m}{D} $
Units are typically g/cm³, g/mL, or g/cm³ (note: 1 mL = 1 cm³).
---
---
#### 1) Brown Sugar Density
> A student measures the mass of an 8 cm³ block of brown sugar to be 12.9 g. What is the density?
- Given:
- Mass $ m = 12.9 $ g
- Volume $ V = 8 $ cm³
- Use:
$$
D = \frac{m}{V} = \frac{12.9\ \text{g}}{8\ \text{cm}^3} = 1.6125\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{1.6125\ \text{g/cm}^3} $ → Correct!
---
#### 2) Cooking Oil Density
> A chef fills a 50 mL container with 43.5 g of cooking oil. What is the density?
- Given:
- $ m = 43.5 $ g
- $ V = 50 $ mL
- $$
D = \frac{43.5}{50} = 0.87\ \text{g/mL}
$$
✔ Answer: $ \boxed{0.87\ \text{g/mL}} $ → Correct!
---
#### 3) Mass of Liquid
> Calculate the mass of a liquid with a density of 2.5 g/mL and a volume of 15 mL.
- Given:
- $ D = 2.5 $ g/mL
- $ V = 15 $ mL
- Use:
$$
m = D \times V = 2.5 \times 15 = 37.5\ \text{g}
$$
✔ Answer: $ \boxed{37.5\ \text{g}} $ → Correct!
---
#### 4) Volume of Liquid
> Calculate the volume of a liquid with a density of 5.45 g/mL and a mass of 65 g.
- Given:
- $ D = 5.45 $ g/mL
- $ m = 65 $ g
- Use:
$$
V = \frac{m}{D} = \frac{65}{5.45} \approx 11.93\ \text{mL}
$$
- Rounded to two decimal places: 11.93 mL
✔ Answer: $ \boxed{11.93\ \text{mL}} $ → Correct! (Note: The handwritten answer says 11.93 mL — correct)
---
#### 5) Aluminum Cube Density
> A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube measures 4 cm, what is the density?
- Side = 4 cm → Volume of cube = $ s^3 = 4^3 = 64\ \text{cm}^3 $
- $ m = 176 $ g
- $$
D = \frac{176}{64} = 2.75\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{2.75\ \text{g/cm}^3} $ → Correct!
---
#### 6) Cork Density
> A piece of cork displaces 23.5 mL of water and has a mass of 5.7 g. What is the density?
- Displacement = volume = 23.5 mL
- Mass = 5.7 g
- $$
D = \frac{5.7}{23.5} \approx 0.2425\ \text{g/mL} \approx 0.24\ \text{g/mL}
$$
✔ Answer: $ \boxed{0.24\ \text{g/mL}} $ → Correct (rounded to two significant figures)
---
#### 7) Granite Block Density
> A granite block weighs 2700 g. Dimensions: 20 cm × 10 cm × 5 cm.
- Volume = $ L \times W \times H = 20 \times 10 \times 5 = 1000\ \text{cm}^3 $
- Mass = 2700 g
- $$
D = \frac{2700}{1000} = 2.7\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{2.7\ \text{g/cm}^3} $ → Correct!
---
#### 8) PVC Pipe Density
> A piece of PVC pipe displaces 60 mL of water and has a mass of 78 g.
- Volume = 60 mL (from displacement)
- Mass = 78 g
- $$
D = \frac{78}{60} = 1.3\ \text{g/mL}
$$
✔ Answer: $ \boxed{1.3\ \text{g/mL}} $ → Correct!
---
#### 9) Magnesium Bar Density
> A solid magnesium bar has a mass of 1300 g and a volume of 743 cm³.
- $$
D = \frac{1300}{743} \approx 1.75\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{1.75\ \text{g/cm}^3} $ → Correct!
---
All solutions on the worksheet are correctly calculated and properly labeled. The student used the appropriate formula, substituted values accurately, and reported units correctly.
---
- Always write down given values.
- Use the formula $ D = \frac{m}{V} $ and rearrange as needed.
- Watch units: mL = cm³, so they can be used interchangeably.
- Round appropriately based on significant figures (e.g., 1.6125 → 1.61 g/cm³ if three sig figs).
---
✔ Conclusion: This worksheet is fully correct and well-executed. Great job!
---
🔷 Density Formula Recap
$$
\text{Density (D)} = \frac{\text{Mass (m)}}{\text{Volume (V)}}
$$
We use this formula in various forms:
- $ D = \frac{m}{V} $
- $ m = D \times V $
- $ V = \frac{m}{D} $
Units are typically g/cm³, g/mL, or g/cm³ (note: 1 mL = 1 cm³).
---
✔ Problem-by-Problem Solution & Explanation
---
#### 1) Brown Sugar Density
> A student measures the mass of an 8 cm³ block of brown sugar to be 12.9 g. What is the density?
- Given:
- Mass $ m = 12.9 $ g
- Volume $ V = 8 $ cm³
- Use:
$$
D = \frac{m}{V} = \frac{12.9\ \text{g}}{8\ \text{cm}^3} = 1.6125\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{1.6125\ \text{g/cm}^3} $ → Correct!
---
#### 2) Cooking Oil Density
> A chef fills a 50 mL container with 43.5 g of cooking oil. What is the density?
- Given:
- $ m = 43.5 $ g
- $ V = 50 $ mL
- $$
D = \frac{43.5}{50} = 0.87\ \text{g/mL}
$$
✔ Answer: $ \boxed{0.87\ \text{g/mL}} $ → Correct!
---
#### 3) Mass of Liquid
> Calculate the mass of a liquid with a density of 2.5 g/mL and a volume of 15 mL.
- Given:
- $ D = 2.5 $ g/mL
- $ V = 15 $ mL
- Use:
$$
m = D \times V = 2.5 \times 15 = 37.5\ \text{g}
$$
✔ Answer: $ \boxed{37.5\ \text{g}} $ → Correct!
---
#### 4) Volume of Liquid
> Calculate the volume of a liquid with a density of 5.45 g/mL and a mass of 65 g.
- Given:
- $ D = 5.45 $ g/mL
- $ m = 65 $ g
- Use:
$$
V = \frac{m}{D} = \frac{65}{5.45} \approx 11.93\ \text{mL}
$$
- Rounded to two decimal places: 11.93 mL
✔ Answer: $ \boxed{11.93\ \text{mL}} $ → Correct! (Note: The handwritten answer says 11.93 mL — correct)
---
#### 5) Aluminum Cube Density
> A machine shop worker records the mass of an aluminum cube as 176 g. If one side of the cube measures 4 cm, what is the density?
- Side = 4 cm → Volume of cube = $ s^3 = 4^3 = 64\ \text{cm}^3 $
- $ m = 176 $ g
- $$
D = \frac{176}{64} = 2.75\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{2.75\ \text{g/cm}^3} $ → Correct!
---
#### 6) Cork Density
> A piece of cork displaces 23.5 mL of water and has a mass of 5.7 g. What is the density?
- Displacement = volume = 23.5 mL
- Mass = 5.7 g
- $$
D = \frac{5.7}{23.5} \approx 0.2425\ \text{g/mL} \approx 0.24\ \text{g/mL}
$$
✔ Answer: $ \boxed{0.24\ \text{g/mL}} $ → Correct (rounded to two significant figures)
---
#### 7) Granite Block Density
> A granite block weighs 2700 g. Dimensions: 20 cm × 10 cm × 5 cm.
- Volume = $ L \times W \times H = 20 \times 10 \times 5 = 1000\ \text{cm}^3 $
- Mass = 2700 g
- $$
D = \frac{2700}{1000} = 2.7\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{2.7\ \text{g/cm}^3} $ → Correct!
---
#### 8) PVC Pipe Density
> A piece of PVC pipe displaces 60 mL of water and has a mass of 78 g.
- Volume = 60 mL (from displacement)
- Mass = 78 g
- $$
D = \frac{78}{60} = 1.3\ \text{g/mL}
$$
✔ Answer: $ \boxed{1.3\ \text{g/mL}} $ → Correct!
---
#### 9) Magnesium Bar Density
> A solid magnesium bar has a mass of 1300 g and a volume of 743 cm³.
- $$
D = \frac{1300}{743} \approx 1.75\ \text{g/cm}^3
$$
✔ Answer: $ \boxed{1.75\ \text{g/cm}^3} $ → Correct!
---
✔ Final Summary
All solutions on the worksheet are correctly calculated and properly labeled. The student used the appropriate formula, substituted values accurately, and reported units correctly.
---
📝 Tips for Students:
- Always write down given values.
- Use the formula $ D = \frac{m}{V} $ and rearrange as needed.
- Watch units: mL = cm³, so they can be used interchangeably.
- Round appropriately based on significant figures (e.g., 1.6125 → 1.61 g/cm³ if three sig figs).
---
✔ Conclusion: This worksheet is fully correct and well-executed. Great job!
Parent Tip: Review the logic above to help your child master the concept of calculate density worksheet.
