Unlocking the Cube: Finding Dimensions from Volume

Algebra 1 Grades High School 3:34 Video
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Lesson Description

Learn how to calculate the side length of a cube when given its volume using cube roots and prime factorization.

Video Resource

Dimensions of a cube from its volume | Numbers and operations | 8th grade | Khan Academy

Khan Academy

Duration: 3:34
Watch on YouTube

Key Concepts

  • Volume of a cube
  • Cube roots
  • Prime factorization

Learning Objectives

  • Students will be able to calculate the side length of a cube given its volume.
  • Students will be able to use prime factorization to find cube roots.
  • Students will be able to relate volume to the dimensions of a cube.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the concept of volume, specifically the formula for the volume of a cube (V = s³). Briefly discuss perfect cubes and the concept of cube roots as the inverse operation of cubing a number.
  • Video Viewing (10 mins)
    Watch the Khan Academy video 'Dimensions of a cube from its volume'. Encourage students to take notes on the presenter's method for finding the side length of a cube, including the use of prime factorization.
  • Guided Practice (15 mins)
    Work through example problems similar to the one in the video. Start with simpler examples (e.g., volume = 27 cubic units) and gradually increase the complexity. Emphasize the steps involved: 1) set up the equation, 2) find the cube root, 3) simplify the cube root using prime factorization if necessary.
  • Independent Practice (15 mins)
    Assign practice problems for students to solve independently. Circulate to provide assistance and answer questions. Encourage students to show their work and explain their reasoning.
  • Wrap-up and Assessment (5 mins)
    Review key concepts and address any remaining questions. Administer a short quiz to assess understanding.

Interactive Exercises

  • Cube Root Challenge
    Provide students with a list of volumes and challenge them to find the corresponding side lengths. Include both perfect cubes and non-perfect cubes to encourage the use of prime factorization.
  • Visual Representation
    Use physical cubes or a digital model to illustrate the relationship between volume and side length. Allow students to manipulate the cubes and visualize the concept.

Discussion Questions

  • What is the relationship between the side length of a cube and its volume?
  • How can prime factorization help us find cube roots?
  • Can you think of real-world scenarios where you might need to calculate the dimensions of a cube given its volume?

Skills Developed

  • Problem-solving
  • Algebraic reasoning
  • Critical thinking

Multiple Choice Questions

Question 1:

The volume of a cube is 64 cubic cm. What is the length of one side?

Correct Answer: 4 cm

Question 2:

What is the cube root of 125?

Correct Answer: 5

Question 3:

The volume of a cube is represented by the equation V = s³, where s is the side length. If V = 216, what is s?

Correct Answer: 6

Question 4:

Which of the following is a perfect cube?

Correct Answer: 27

Question 5:

What is the prime factorization of 8?

Correct Answer: 2 x 2 x 2

Question 6:

If the side length of a cube is 3 cm, what is its volume?

Correct Answer: 27 cubic cm

Question 7:

Which of the following represents 'x cubed'?

Correct Answer: x * x * x

Question 8:

What is the cube root of 1?

Correct Answer: 1

Question 9:

A cube has a volume of 1000 cubic meters. What is the measure of one side?

Correct Answer: 10 meters

Question 10:

The side length of a cube is represented by 'a'. What expression represents the volume of the cube?

Correct Answer: a³

Fill in the Blank Questions

Question 1:

The volume of a cube is found by cubing the length of its ____.

Correct Answer: side

Question 2:

The cube root of 8 is ____.

Correct Answer: 2

Question 3:

If V = s³, then s = the ____ root of V.

Correct Answer: cube

Question 4:

A perfect cube is a number that can be obtained by cubing a(n) ____ number.

Correct Answer: integer

Question 5:

Prime ____ is a method to break down a number into its prime factors.

Correct Answer: factorization

Question 6:

The cube root of 27 is ____.

Correct Answer: 3

Question 7:

A cube with sides of length 5 has a volume of _____.

Correct Answer: 125

Question 8:

If a cube has a volume of 1,728 cubic meters, each side measures _____ meters.

Correct Answer: 12

Question 9:

x * x * x can be written as x to the ____ power.

Correct Answer: third

Question 10:

Finding the side length of a cube when you know its volume involves calculating the ____ root.

Correct Answer: cube

Educational Standards

A1.N.1:[Standard] Extend the understanding of exponents to include square roots and cube roots. A1.N.1.1:[Objective] Write square roots and cube roots of constants and monomial algebraic expressions in simplest radical form. A1.A.3.4:[Objective] Evaluate linear, absolute value, rational, and radical expressions. Include applying a nonstandard operation such as x ⨀ y=2x+y.

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