courses › Geometry

Area, circumference, and slices of a circle, in terms of π.

In your head, jot if needed · no calculator why?

Learn first (about 3 minutes)

Opens at level 22.

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Builds on: Area & perimeter (not open yet)

skills · practice stats

From rounds of this course only: box, review and trial answers are left out. Once a skill has 40 tries, it compares your first 20 tries with your last 20.

• Circle area par 13 s not tried yet

  worked example

  A circle has diameter 2. Its area is kπ. What is k?

  Answer: 1

  1. The radius is half the diameter: 1.
  2. Area = πr² = 1² × π = π, so k = 1.

• Circumference par 9 s not tried yet

  worked example

  A circle has diameter 15. Its circumference is kπ. What is k?

  Answer: 15

  1. Circumference = πd = 15π, so k = 15.

• Sectors & arcs par 20 s not tried yet

  worked example

  A sector of a circle has radius 2 and a central angle of 45°. Its area is kπ. What is k? Give k as a whole number or a fraction.

  Answer: 1/2

  1. 45° is 1/8 of a full turn.
  2. The whole circle's area is 2² × π = 4π.
  3. The sector is 1/8 × 4π = (1/2)π, so k = 1/2.

rest ladder

Win 3 of your last 4 rounds and the course rests. A win is 90% right, within 2× the round's par. Pass the review when it comes back and the next rest is longer.

1. 1 day
2. 3 days
3. 7 days
4. 14 days
5. 30 days
6. 60 days
7. mastered · every 90 days

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