Learn with Amar
Teaching video
A teaching recording for this chapter has not been published yet. Start with the worked example below and explore the related animations where available.
Grade 10 chapters and video availability01 · Read and understand
What you will learn
- Find arc length and sector area from a central angle in degrees.
- Justify the method and check its domain, units, or logical conditions.
Before you start
Algebraic equations, ratios, angle and area facts, and basic coordinate geometry.
Keep paper nearby. Read the question once for the context, then again to identify what is known and what you need to find.
Start with a question
A circle has radius 6 cm and a sector angle of 120°. Find its arc length and area.
Why this math matters
Separate curved boundary material from the surface area enclosed by a circular sector. The example connects a stated condition to a conclusion and then checks whether the result satisfies that condition.
Set up the model
A useful answer starts with clear assumptions:
- Use Euclidean geometry and the angle, parallelism, similarity, or congruence conditions stated; a sketch alone does not establish them.
- Treat provided measurements as exact classroom-model values unless an approximation or uncertainty is stated.
02 · Work through the example
Follow the reasoning, one step at a time.
Try to predict the next step before reading it. After each calculation, explain why the operation makes sense and how it helps answer the original question.
Work through it with Amar
See this example unfold.
The complete worked example, one idea at a time.
Use the same turn fraction for arc and sector
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A circle has radius 6 cm and a sector angle of 120°. Find its arc length and area.
Before you calculate
Read what is known and what you need to find. Make a prediction before moving to the first calculation.
Starts paused. Play advances through the full text at a reading pace; pause whenever you need more time. Previous, Next, and the phase buttons let you set your own pace. Playback pauses when this walkthrough leaves the screen or you switch tabs.
Your device’s reduced-motion setting keeps each phase still. Manual controls remain available. The full written solution stays below.
Represent the conditions
Turn fraction = 120/360 = 1/3
The sector occupies one third of a complete circle.
Develop the calculation
Arc = (1/3)(2π·6)=4π cm
Apply that fraction to circumference for a boundary length.
Check and interpret
Sector area = (1/3)(π·6²)=12π cm²
The same fraction of the disk gives an area, which uses different units.
The result
Sector area = (1/3)(π·6²)=12π cm²
The same fraction of the disk gives an area, which uses different units.
Common mistakes to catch
- Use circumference for arc length and disk area for sector area.
- The degree fraction is angle/360, not angle/180.
03 · Practice independently
Try it before revealing the answer.
Use paper or a calculator as needed. Write your units and reasoning, then open the hint or explanation to check your approach.
Practice 1
Find the arc length of a 90° sector with radius 8 m.
Show a hint
Take one quarter of the circumference.
Reveal answer and explanation
4π m
(1/4)(16π)=4π.
Practice 2
Does doubling radius at a fixed sector angle double both arc and area?
Show a hint
Compare the r and r² dependencies.
Reveal answer and explanation
Arc doubles; area quadruples
The angular fraction stays constant while length and area scale differently.
Take the idea with you
Separate curved boundary material from the surface area enclosed by a circular sector.
04 · Reflect and continue
Can you explain it in your own words?
Before moving on, explain the main idea without looking at the worked example. Try both practice questions, check your reasoning, and name one mistake you now know how to avoid. Return to a step if you still need support.
Up next: Derive distance from horizontal and vertical changes
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