Card 1 of 20
EasyStudy card 1
Prompt
What is the circumference formula using radius?
Answer
\(C=2\pi r\).
MathChapter 19: Circles
Flashcards
Arc Lengths and Areas of Sectors Flashcards
Twenty concise cards on circle fractions, arcs, sectors, radians, and wheel travel.
Current card1 / 20
Session progress0 of 20 studied
Card 1 of 20. Answer hidden.
Card 2 of 20
EasyStudy card 2
Prompt
What is the circumference formula using diameter?
Answer
\(C=\pi d\).
Card 3 of 20
EasyStudy card 3
Prompt
What is the area formula for a circle?
Answer
\(A=\pi r^2\).
Card 4 of 20
EasyStudy card 4
Prompt
What is a sector?
Answer
A region bounded by two radii and their intercepted arc.
Card 5 of 20
EasyStudy card 5
Prompt
What fraction of a circle does θ degrees represent?
Answer
\(\theta/360\).
Card 6 of 20
EasyStudy card 6
Prompt
What is the degree arc-length formula?
Answer
\(L=(\theta/360)(2\pi r)\).
Card 7 of 20
EasyStudy card 7
Prompt
What is the degree sector-area formula?
Answer
\(A_s=(\theta/360)(\pi r^2)\).
Card 8 of 20
MediumStudy card 8
Prompt
How are angle, arc, and sector fractions related?
Answer
They are the same fraction of their respective wholes.
Card 9 of 20
MediumStudy card 9
Prompt
What is the arc-length formula in radians?
Answer
\(L=r\theta\), when θ is in radians.
Card 10 of 20
MediumStudy card 10
Prompt
What is the sector-area formula in radians?
Answer
\(A_s=\tfrac12r^2\theta\).
Card 11 of 20
MediumStudy card 11
Prompt
What distance does a wheel travel in n revolutions?
Answer
\(D=2\pi rn\), assuming no slipping.
Card 12 of 20
MediumStudy card 12
Prompt
What units should arc length have?
Answer
Linear units.
Card 13 of 20
MediumStudy card 13
Prompt
What units should sector area have?
Answer
Square units.
Card 14 of 20
MediumStudy card 14
Prompt
What is a 72° sector as a circle fraction?
Answer
One fifth.
Card 15 of 20
MediumStudy card 15
Prompt
Why keep π exact during work?
Answer
It prevents rounding drift and usually matches SAT answer form.
Card 16 of 20
MediumStudy card 16
Prompt
What must happen before a wheel calculation with mixed units?
Answer
Convert all lengths to one unit.
Card 17 of 20
HardStudy card 17
Prompt
Radius 12, angle 150°: arc length?
Answer
\(10\pi\).
Card 18 of 20
HardStudy card 18
Prompt
Radius 12, angle 150°: sector area?
Answer
\(60\pi\).
Card 19 of 20
HardStudy card 19
Prompt
A sector perimeter includes which three boundary pieces?
Answer
Two radii and one arc.
Card 20 of 20
HardStudy card 20
Prompt
A semicircle perimeter includes what easy-to-miss piece?
Answer
The diameter, in addition to half the circumference.
Deck complete
You rated every card. Revisit difficult cards or shuffle for another pass.
Keyboard: Space reveals, left/right arrows navigate, 1–4 rate, and S shuffles.