Let’s go through each problem step by step, correcting any errors and explaining the reasoning clearly.
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Problem 4:
> *Consider the volume occupied by a cubic container (jar) compared with the volume occupied by a cuboid jar?*
Hint: They are the same.
✔ Explanation:
This question is testing your understanding of
volume as a measure of space — not shape. A “cubic container” means a cube (all sides equal), and a “cuboid jar” means a rectangular prism (sides may differ).
But the hint says: *“They are the same.”* That implies that both containers have the
same volume, even though their shapes differ.
➡️
Key Concept: Volume depends on dimensions, not shape. Two objects can have different shapes but occupy the same amount of space (same volume). For example, a cube of side 2 cm has volume 8 cm³; a cuboid of 1 cm × 2 cm × 4 cm also has volume 8 cm³.
So, the answer is:
>
The volumes are the same if their dimensions result in equal volume, regardless of shape.
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Problem 5:
> *A rock occupies a volume of 20 cm³ and has a mass of 54 grams. Find the density of this rock.*
You wrote:
> *54/20 = 2.7 g/cm³*
✔ Correct!
Formula for density:
>
Density = Mass / Volume
Plug in:
> Density = 54 g / 20 cm³ =
2.7 g/cm³
This is a reasonable density for many types of rocks (e.g., granite is around 2.6–2.7 g/cm³).
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Problem 6:
> *Water has a density of 1.0 g/mL and ocean water has a density of 1.025 g/mL. Why are they different?*
You wrote:
> *Ocean water contains salt.*
✔ Correct explanation!
Why it matters:
- Pure water (H₂O) has a density of 1.0 g/mL at 4°C.
- Ocean water contains dissolved salts (mainly NaCl), which add mass without adding much volume.
- More mass in the same volume → higher density.
➡️ So,
salt increases the mass per unit volume, making ocean water denser than fresh water.
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Problem 7:
> *A student measures the mass of 8 mL of iron sugar to be 12.9 grams. What is the density of the brown sugar?*
You wrote:
> *12.9/8 = 1.6125 = 1.61 g/mL*
⚠️
Almost correct — but there’s a typo!
It says “iron sugar” — that’s probably a typo. It should be
“brown sugar” (as mentioned at the end).
Assuming that’s the case, your calculation is correct:
> Density = Mass / Volume = 12.9 g / 8 mL =
1.6125 g/mL
Rounded to two decimal places:
1.61 g/mL
✔ Answer: 1.61 g/mL
*(Note: Brown sugar typically has a density around 0.8–0.9 g/mL when loosely packed, but if this is a lab measurement, we accept the given data. Perhaps it was packed tightly or measured differently.)*
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✔ Final Answers Summary:
4. The volumes are the same if the containers hold equal amounts of space, regardless of shape (cube vs. cuboid).
5. Density = 54 g / 20 cm³ =
2.7 g/cm³
6. Ocean water is denser because it contains dissolved salts, which increase mass without significantly increasing volume.
7. Density = 12.9 g / 8 mL =
1.61 g/mL *(assuming “iron sugar” was meant to be “brown sugar”)*
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Let me know if you’d like diagrams or more detailed explanations for any part!
Parent Tip: Review the logic above to help your child master the concept of density problems worksheet with answers.
