Seventh Grade · Math · week 29

Area and circumference formulas

Apply the formulas C = pi x d (or 2 x pi x r) and A = pi x r^2 to find the circumference and area of a circle.

Now that pi is familiar, two formulas handle every circle problem: circumference C = pi x d, which is the same as 2 x pi x r since the diameter is twice the radius; and area A = pi x r^2, radius squared times pi.

Circumference measures distance AROUND a circle (a length), while area measures the space INSIDE it (in square units). Reading a problem carefully to see which one is being asked for matters as much as the formula itself.

📋 For the teacher
Teach it (10–15 min):
  • Keep both formulas posted side by side this week, and underline the "squared" in the area formula -- it is the single most common mix-up.
  • Ask "distance around, or space inside?" before starting any circle problem, to decide which formula applies.
  • Practice working backwards, finding the radius from a given circumference or area, not just the forward direction.
  • Keep the exact form (like 36 x pi) visible next to the decimal estimate -- both are correct, valuable answers.
Talk about it:
  • What is the difference between what circumference and area each measure?
  • Why does the area formula square the radius but the circumference formula does not?
  • How would you find the radius if you were only given the circumference?

Mastery looks like: They correctly compute circumference and area from a radius or diameter, and work backwards to find a radius when needed.

Common stumbles: Squaring the radius when finding circumference (or forgetting to square it for area); confusing radius and diameter in either formula.

Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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