Friday
Friday: Circles Everywhere
Rocket rolls the can across the Blueprint Table. One turn, and he marks where it stops. "Look at that."
Raven measures from start to mark. "About 25 centimeters. One turn rolls one circumference. What do you notice?"
"A wheel does the same," Rocket says. "Every turn moves it one circumference forward. I could count turns to measure the garage."
"Round tabletops, clock faces, plates, pipes," Raven says. "Every one has a radius, a circumference and an area."
Nova hovers beside the rolling can, her light following its rim. "Edge or inside?" she says. "That is the only question."
"Edge means C, inside means A," Rocket says. Nova hums. "Next week, the roof angles. Find the protractor."
Edge or inside?
| Everyday question | Edge or inside? | Formula |
|---|---|---|
| How far does a wheel roll in one turn? | edge | C = π × d |
| How much tape goes around a round lid? | edge | C = 2 × π × r |
| How much paper covers a round tabletop? | inside | A = πr² |
| How much clear sheet fills the round window? | inside | A = πr² |
Ask "edge or inside?" first. Distance around is circumference, in centimeters. Space inside is area, in square centimeters.
The two are linked. Half of C times r gives A. For radius 5: ½ × 31.4 × 5 = 78.5, and 3.14 × 5 × 5 = 78.5. Same number.
The week in four lines
- d = 2 × r. The diameter is twice the radius.
- C = π × d = 2 × π × r. The circumference is a little more than three diameters.
- A = πr². The area is half the circumference times the radius, from the wedge rectangle.
- Use 3.14 for π. Lengths in centimeters, areas in square centimeters.
- Read the question.
- Tap your answer.
A toy wheel has diameter 30 cm. How far does it roll in one full turn, in centimeters? (Use 3.14 for π.)
A round tabletop has radius 20 cm. How much tape goes once around its edge, in centimeters? (Use 3.14 for π.)The same tabletop has radius 20 cm. How much paper covers it, in square centimeters? (Use 3.14 for π.)- Read the question.
- Tap your answer.
A circle has diameter 14 cm. What is its circumference in centimeters? (Use 3.14 for π.)
A circle has radius 4 cm. What is its area in square centimeters? (Use 3.14 for π.)
A circle has radius 7 cm. What is its circumference in centimeters? (Use 3.14 for π.)| Week review | True or false? |
|---|---|
| The radius is twice the diameter. | ? |
| The circumference is a little more than three diameters. | ? |
| 2 × 3.14 × 10 = 62.8 | ? |
| 3.14 × 4 × 4 = 50.24 | ? |
| Area is measured in centimeters. | ? |
- ?We measured four round things in Build Lab and compared the divisions.
- ?We wrapped string around the can and found a little more than three diameters.
- ?We wrote C = π × d and C = 2 × π × r, and ran them backward.
- ?We cut a circle into wedges and found A = πr².
Measure one diameter and work out both the circumference and the area in your Blueprint Book.
Edge or inside, you can answer both now. Tomorrow is Build Day: the round window goes on the clubhouse.