Predict mass from density

Supplied materials

• All measurements and observations below are supplied classroom examples. They are not data from actual learners or a claim about a particular real site.
• Paper or browser document; an ordinary calculator is optional.
• Rule: Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. Formula: a*b. Variable key: a = density (g/cm³), b = volume (cm³)
• Distinct worked inputs and result: A distinct uniform model has density 3 g/cm³ and volume 5 cm³: 3×5=15 g.
• Assessment case 1: Supplied case 1: density (g/cm³)=2; volume (cm³)=8, using the explicitly named quantities. Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. What result follows?
• Assessment case 2: Supplied case 2: density (g/cm³)=3; volume (cm³)=7, using the explicitly named quantities. Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. What result follows?
• Assessment case 3: Supplied case 3: density (g/cm³)=4; volume (cm³)=9, using the explicitly named quantities. Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. What result follows?
• Assessment case 4: Supplied case 4: density (g/cm³)=5; volume (cm³)=6, using the explicitly named quantities. Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. What result follows?
• Assessment case 5: Supplied case 5: density (g/cm³)=6; volume (cm³)=4, using the explicitly named quantities. Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. What result follows?
• Assessment case 6: Supplied case 6: density (g/cm³)=2.5; volume (cm³)=12, using the explicitly named quantities. Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. What result follows?

Learn the idea

For a uniform sample at stated conditions, mass scales with volume. A density model can predict mass, but it does not identify every unknown material uniquely.

Mass equals density in grams per cubic centimeter multiplied by volume in cubic centimeters. The formula in the supplied model is a*b. Variable key: a = density (g/cm³), b = volume (cm³). Multiply density by volume. The volume unit must match the density denominator.

A distinct uniform model has density 3 g/cm³ and volume 5 cm³: 3×5=15 g. Use the stated uniform-material assumption. Track the quantity and unit before calculating. Explain the meaning of a positive, negative or fractional result when relevant. A numerical answer supports the stated model calculation; broader claims require the additional measurements and assumptions described here.

1. Name the measured quantities and their units before substituting values.
2. Write the stated rule and use the variable key to match each symbol to its explicitly named quantity.
3. Calculate each supplied case separately, keeping intermediate arithmetic and the result unit.
4. Explain the result in context and identify the assumption that would invalidate direct use of the rule.

Check your reasoning

Your answer is temporary and is not saved to an account. Download your current answer before leaving or reloading. Written work on paper or in another app stays in your own file.

Take it further

Changed-input task: use the same stated model with density (g/cm³)=3; volume (cm³)=8. Expected result: 24 g. Explain what changes and keep this assumption: Use the stated uniform-material assumption.

Nothing here is saved to an account or sent to a teacher. The answer download includes your current choice and any checked feedback. It does not include choices from the separate More practice section. Download that section separately.