Concentric Circles

Learning Resource Type

Classroom Resource

Subject Area

Mathematics

Grade(s)

7

Overview

In this video you’ll discover how using concentric circles can help you determine how much paint is needed to cover the deck of a carousel. Regents Review materials are designed to help high school students prepare for New York State's Regents exams.

Mathematics (2019) Grade(s): 7

MA19.7.20

Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

UP:MA19.7.20

Vocabulary

  • Diameter
  • Radius
  • Circle
  • Area
  • Circumference
  • π

Knowledge

Students know:
  • that the ratio of the circumference of a circle and its diameter is always π.
  • The formulas for area and circumference of a circle.

Skills

Students are able to:
  • use the formula for area of a circle to solve problems.
  • Use the formula(s) for circumference of a circle to solve problems.
  • Give an informal derivation of the relationship between the circumference and area of a circle.

Understanding

Students understand that:
  • area is the number of square units needed to cover a two-dimensional figure.
  • Circumference is the number of linear units needed to surround a circle.
  • The circumference of a circle is related to its diameter (and also its radius).
Mathematics (2019) Grade(s): 7 - Grade 7 Accelerated

MA19.7A.36

Explain the relationships among circumference, diameter, area, and radius of a circle to demonstrate understanding of formulas for the area and circumference of a circle.

UP:MA19.7A.36

Vocabulary

  • Diameter
  • Radius
  • Circle
  • Area
  • Circumference
  • π

Knowledge

Students know:
  • the ratio of the circumference of a circle and its diameter is always π.
  • The formulas for area and circumference of a circle.

Skills

Students are able to:
  • use the formula for area of a circle to solve problems.
  • Use the formula(s) for circumference of a circle to solve problems.
  • Give an informal derivation of the relationship between the circumference and area of a circle.

Understanding

Students understand that:
  • area is the number of square units needed to cover a two-dimensional figure.
  • Circumference is the number of linear units needed to surround a circle.
  • The circumference of a circle is related to its diameter (and also its radius).

CR Resource Type

Audio/Video

Resource Provider

PBS

License Type

PD
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