Mass and volume as a rate

About this lesson

Grade 6 › Unit rates and percentages

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Mass and volume as a rate

Warm-up

Three quick questions from earlier lessons.

Discover

1 cm³ of iron has a mass of about 8 g. About what is the mass of 5 cm³ of iron?

  1. 40 g
  2. 13 g

Key idea

Mass and volume form a rate.

For one material, mass and volume are proportional. The mass per unit of volume (grams per cm³) is a unit rate: mass = rate × volume, and rate = mass ÷ volume. A larger rate means a denser material.

Worked example

A 6 cm³ piece of a metal has a mass of 54 g.

54 ÷ 6 = 9 g per cm³
Unit rate.
9 × 10 = 90 g
Mass of 10 cm³.

Your turn, guided

Your turn: 1 cm³ of a wood has a mass of 3 g. Mass of 12 cm³?

3636 g
3 × 12.

Practice ★

  1. Each cubic centimeter of a metal has a mass of 5 grams. What is the mass, in grams, of a piece with a volume of 6 cm³?
  2. Each cubic centimeter of a metal has a mass of 4 grams. What is the mass, in grams, of a piece with a volume of 14 cm³?
  1. A stone has a mass of 8 grams and a volume of 4 cm³. What is the mass of 1 cm³ of the stone, in grams?

Watch out!

Practice ★★

  1. Block A has a mass of 108 g and a volume of 27 cm³. Block B has a mass of 12 g and a volume of 2 cm³. Which block is made of the denser material (more grams per cm³)?
    1. Block B
    2. Block A, because it has the greater mass
    3. Neither: the masses tell us nothing about it
  2. Block A has a mass of 84 g and a volume of 28 cm³. Block B has a mass of 14 g and a volume of 2 cm³. Which block is made of the denser material (more grams per cm³)?
    1. Block B
    2. Block A, because it has the greater mass
    3. Neither: the masses tell us nothing about it
  1. A stone has a mass of 8 grams and a volume of 4 cm³. What is the mass of 1 cm³ of the stone, in grams?

Exit ticket

Three questions to check you have got it.

  1. Each cubic centimeter of a metal has a mass of 5 grams. What is the mass, in grams, of a piece with a volume of 6 cm³?
  2. Each cubic centimeter of a metal has a mass of 4 grams. What is the mass, in grams, of a piece with a volume of 14 cm³?
  3. Each cubic centimeter of a metal has a mass of 3 grams. What is the mass, in grams, of a piece with a volume of 4 cm³?

Summary card

Mass and volume

Grams per cm³ = mass ÷ volume; mass = grams per cm³ × volume.

Watch out: divide mass by volume, not volume by mass.

End of the lesson

Next lesson: Percent of a quantity; finding the percent and the whole Back to the chapter

Answers: Mass and volume as a rate

A

  1. 3030
  2. 5656

B

  1. 22

C

  1. Block B
  2. Block B

D

  1. 22

E

  1. 3030
  2. 5656
  3. 1212

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