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 relate a wheel's turns to circumference.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Multiplication and the meaning of diameter.
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
An ideal wheel has diameter 0.8 m. How far does its centre travel in 5 full turns without slipping? Give an exact answer and a two-decimal approximation.
Why this math matters
One full turn of an ideal rolling wheel covers one circumference, which is π times its diameter. For a rolling model, state the no-slip assumption before turning rotations into distance.
Set up the model
A useful answer starts with clear assumptions:
- The wheel rolls on a straight flat path without slipping.
- The wheel is circular with a constant 0.8 m diameter.
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.
Relate a wheel's turns to circumference
PausedQuestion: Start with the question. Paused.
Question
Start with the question
An ideal wheel has diameter 0.8 m. How far does its centre travel in 5 full turns without slipping? Give an exact answer and a two-decimal approximation.
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
C = πd = 0.8π m
Circumference is the distance traveled in one complete turn.
Apply the relationship
distance = 5(0.8π) = 4π m
Multiply the distance per turn by the number of turns.
Check and interpret
4π m ≈ 12.57 m
Keep π until the last step to avoid accumulating rounding error.
The result
4π m ≈ 12.57 m
Keep π until the last step to avoid accumulating rounding error.
Common mistakes to catch
- Using πr instead of 2πr gives half the circumference.
- πr² measures area rather than distance around a circle.
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
A circle has radius 3 cm. What is its circumference?
Show a hint
The diameter is twice the radius.
Reveal answer and explanation
6π cm
C = 2πr = 2π(3).
Practice 2
An ideal wheel with circumference 1.5 m travels 12 m. How many turns does it make?
Show a hint
Divide total distance by distance per turn.
Reveal answer and explanation
8 turns
12/1.5 = 8.
Take the idea with you
For a rolling model, state the no-slip assumption before turning rotations into distance.
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: Use the radius to find a circular area
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