Math Problem Statement

Ravi has a 0.5 gram sample of the mineral goslarite. He knows that goslarite has a density of 2.00 grams per cubic centimeter. He wants to use this information to determine the volume of the mineral sample. Which statement about Ravi's sample is true?

Solution

We are tasked with determining the correct volume of Ravi's sample using the provided formula for density:

D=mVD = \frac{m}{V}

Where:

  • D=2.00g/cm3D = 2.00 \, \text{g/cm}^3 (density of goslarite),
  • m=0.5gm = 0.5 \, \text{g} (mass of the sample),
  • VV is the unknown volume.

To isolate VV, rearrange the formula:

V=mDV = \frac{m}{D}

Substituting the values:

V=0.52.00=0.25cm3V = \frac{0.5}{2.00} = 0.25 \, \text{cm}^3

Correct Answer:

Option A: The volume is 0.25 cubic centimeters because V=mDV = \frac{m}{D}.


Do you need further details or clarification?

Here are 5 related questions to extend your understanding:

  1. How is density related to mass and volume?
  2. If the density increases but mass stays constant, what happens to the volume?
  3. If Ravi's sample mass were doubled, what would the new volume be?
  4. How would you find the mass if density and volume were provided?
  5. Can you plot a graph showing the relationship between mass, volume, and density?

Tip: Always check the units when substituting values into formulas to ensure they are consistent!

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Math Problem Analysis

Mathematical Concepts

Density, Mass, and Volume Relationship
Algebraic Manipulation

Formulas

D = m / V
V = m / D

Theorems

Rearrangement of equations using algebra

Suitable Grade Level

Grades 6-8