calculate the volume of 5250 kilograms of wood if the density of wood is 750 kg/m^{3}.
Calculate the Volume of Wood
RULE / FORMULA USED: The relationship between density, mass, and volume is given by the formula:
\text{Density} (\rho) = \frac{\text{Mass} (m)}{\text{Volume} (V)}
From this, we can derive the formula to find the volume:
\text{Volume} (V) = \frac{\text{Mass} (m)}{\text{Density} (\rho)}
SOLUTION STEPS:
Step 1 — Identify Given Values
We are given:
- Mass (m) = 5250 \text{ kg}
- Density (\rho) = 750 \text{ kg/m}^3
Step 2 — Substitute Values into the Formula
Substitute the given mass and density values into the volume formula:
V = \frac{5250 \text{ kg}}{750 \text{ kg/m}^3}
Step 3 — Perform the Calculation
Divide the mass by the density to find the volume:
V = 7 \text{ m}^3
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ANSWER: The volume of the wood is 7 \text{ m}^3.
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KEY CONCEPTS:
1. Density (\rho)
- Definition: Density is a measure of how much mass is contained in a given unit volume. It indicates how “compact” a substance is.
- In this problem: We used the known density of wood (750 \text{ kg/m}^3) to determine the space occupied by a specific mass of that wood.
2. Mass (m)
- Definition: Mass is a fundamental property of matter, representing the amount of “stuff” in an object. It is a measure of an object’s inertia.
- In this problem: The given mass of wood (5250 \text{ kg}) was the total amount of wood we were considering.
3. Volume (V)
- Definition: Volume is the amount of three-dimensional space occupied by an object or substance.
- In this problem: We calculated the volume occupied by the 5250 \text{ kg} of wood, which came out to be 7 \text{ m}^3.
COMMON MISTAKES:
Confusing Mass and Volume
- Wrong: Assuming that a larger mass always means a larger volume without considering density, or directly equating mass to volume.
- Right: Understanding that mass is the amount of matter, and volume is the space it occupies. Density connects these two.
- Why it’s wrong: Two objects can have the same mass but vastly different volumes if their densities differ (e.g., a feather and a rock).
Incorrect Formula Rearrangement
- Wrong: Accidentally using V = m \times \rho or \rho = V / m.
- Right: Always remember or derive the correct formula: \rho = m/V, so V = m/\rho and m = \rho \times V.
- Why it’s wrong: Using an incorrect formula will lead to a numerically wrong answer with incorrect units.
Would you like me to generate a similar practice problem to test your skills?