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Geometry and Measurement 6-8 / Week 07 / Tuesday
2/6
Week 07 · Circles

Tuesday

C equals pi times d
// String around a can, and a little more than three
⏱ about 20 min

Tuesday: C Equals Pi Times d

Raven pins a card to the Blueprint Table: C = π × d. "One formula for every round thing."

"And if I only know the radius?" Rocket asks, holding the small lid by its middle.

"Then double it first," Raven says. "Or write C = 2 × π × r. What do you notice? It is the same rule."

Rocket tries the lid. "Radius 5. Two times 3.14 times 5." He works it on the pad. "31.4 centimeters."

Nova hovers over the formula card, her light steady. "Now go backward," she says. "If the string says 62.8, how wide is the circle?"

"Divide by 3.14," Rocket says slowly. "Twenty." Nova hums. "The formula runs both ways."

Two ways to write one formula

You knowFormulaExampleCircumference
the diameterC = π × dd = 10 cm3.14 × 10 = 31.4 cm
the radiusC = 2 × π × rr = 5 cm2 × 3.14 × 5 = 31.4 cm
the circumferenced = C ÷ πC = 62.8 cm62.8 ÷ 3.14 = 20 cm

Both formulas say the same thing, because 2 × r is the diameter. Pick the one that matches what you measured.

Always use 3.14 for π in this course. Write the units: centimeters for a length around, never square centimeters.

  1. Write down what you know: radius or diameter, with units.
  2. If you have the radius, double it to get the diameter, or use 2 × π × r.
  3. Multiply by 3.14.
  4. Check: the answer should be a little more than three diameters.
A circle with a radius of 6 cm marked from the center to the edge

Check the picture: radius 6 cm, so diameter 12 cm. C = 2 × 3.14 × 6 = 37.68 cm. Three twelves are 36, and 37.68 is a little more. It checks.

FROM THE DIAMETER
  • Read the question.
  • Tap your answer.
A circle with diameter 12 cmA circle has diameter 12 cm. What is its circumference in centimeters? (Use 3.14 for π.)
A circle with diameter 20 cmA circle has diameter 20 cm. What is its circumference in centimeters? (Use 3.14 for π.)
A circle with diameter 7 cmA circle has diameter 7 cm. What is its circumference in centimeters? (Use 3.14 for π.)
A circle with diameter 2.5 cmA circle has diameter 2.5 cm. What is its circumference in centimeters? (Use 3.14 for π.)
FROM THE RADIUS
  • Read the question.
  • Tap your answer.
A circle with radius 5 cmA circle has radius 5 cm. What is its circumference in centimeters? (Use 3.14 for π.)
A circle with radius 6 cmA circle has radius 6 cm. What is its circumference in centimeters? (Use 3.14 for π.)
A circle with radius 10 cmA circle has radius 10 cm. What is its circumference in centimeters? (Use 3.14 for π.)
A circle with radius 3.5 cmA circle has radius 3.5 cm. What is its circumference in centimeters? (Use 3.14 for π.)
BACKWARD FROM THE STRING
  • Read the question.
  • Tap your answer.
A circle has circumference 62.8 cm. What is its diameter in centimeters? (Use 3.14 for π.)
A circle has circumference 31.4 cm. What is its diameter in centimeters? (Use 3.14 for π.)
The string around a lid measures 15.7 cm. Using 3.14 for π, what is the lid's diameter in centimeters?
StatementTrue or false?
3.14 × 10 = 31.4?
2 × 3.14 × 4 = 25.12?
3.14 × 6 = 37.68?
The circumference is a little more than three diameters.?
WHY THIS EXERCISEMixing up radius and diameter doubles or halves the answer. The "three diameters" check catches it.
Try it
Measure the diameter of two round lids at home. Predict each circumference with 3.14 before you wrap string.
Then wrap the string and compare. How close was each prediction?
Safety first
Lids are plastic or smooth metal with no sharp edge. A grown-up checks each one first.
String stays on the table for measuring, never around anyone's neck.

Two formulas, one idea. Tomorrow is Build Lab: string around every round thing in the garage.

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