Learn with Amar
Teaching video
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Grade 7 chapters and video availability01 · Read and understand
What you will learn
- Explain how to use the radius to find a circular area.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Radius, diameter, and squaring.
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 circular design has diameter 14 cm. Find its area, then determine the area factor if the diameter is doubled.
Why this math matters
Circular area scales with the square of the radius, making a length change larger in area terms. Compare areas of circular designs by squaring their radius ratio.
Set up the model
A useful answer starts with clear assumptions:
- The design is a flat circular region.
- The enlargement preserves the circular shape.
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 radius to find a circular area
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A circular design has diameter 14 cm. Find its area, then determine the area factor if the diameter is doubled.
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 quantities
r = 14/2 = 7 cm
Area uses the radius; the given diameter must first be halved.
Apply the relationship
A = πr² = 49π cm²
Squaring the radius produces square centimetres.
Check and interpret
new area = π(14)² = 196π cm² = 4A
Doubling every length quadruples circular area.
The result
new area = π(14)² = 196π cm² = 4A
Doubling every length quadruples circular area.
Common mistakes to catch
- Putting a diameter directly into πr² overestimates area by a factor of four.
- A doubled radius does not produce only twice the area.
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 area of a circle with radius 5 m.
Show a hint
Square the radius before multiplying by π.
Reveal answer and explanation
25π m²
A = π(5²) = 25π.
Practice 2
A circle's area is 81π cm². Find its diameter.
Show a hint
Solve r² = 81, taking the positive radius.
Reveal answer and explanation
18 cm
r = 9 cm, so d = 2r = 18 cm.
Take the idea with you
Compare areas of circular designs by squaring their radius ratio.
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: Find an L-shaped area by subtraction
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