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 8 chapters and video availability01 · Read and understand
What you will learn
- Explain how to build a cylinder from circular layers.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Circle area and prism-style volume.
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 closed cylindrical model has radius 3 cm and height 8 cm. Find its internal geometric volume, ignoring wall thickness.
Why this math matters
A cylinder's volume is its circular base area multiplied by its perpendicular height. Recover either height or radius from a stated cylinder volume by isolating the missing factor.
Set up the model
A useful answer starts with clear assumptions:
- The cylinder has a constant circular cross-section.
- The listed radius and height are interior dimensions; wall thickness is ignored.
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.
Build a cylinder from circular layers
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A closed cylindrical model has radius 3 cm and height 8 cm. Find its internal geometric volume, ignoring wall thickness.
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
base area = πr² = π(3²) = 9π cm²
A perpendicular cross-section is a circle of radius 3 cm.
Apply the relationship
V = base area × height = 9π × 8
Extending the constant area through 8 cm gives the volume.
Check and interpret
V = 72π cm³ ≈ 226.19 cm³
The exact answer retains π; the decimal is rounded to two places.
The result
V = 72π cm³ ≈ 226.19 cm³
The exact answer retains π; the decimal is rounded to two places.
Common mistakes to catch
- Cylinder volume uses πr²h, not circumference times height.
- A diameter must be halved before squaring in the radius formula.
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 cylinder has diameter 10 m and height 2 m. Find its volume.
Show a hint
Convert diameter to radius first.
Reveal answer and explanation
50π m³
r = 5; π(5²)(2) = 50π.
Practice 2
A cylinder's volume is 45π cm³ and its radius is 3 cm. Find its height.
Show a hint
Divide volume by base area.
Reveal answer and explanation
5 cm
h = 45π/(9π) = 5.
Take the idea with you
Recover either height or radius from a stated cylinder volume by isolating the missing factor.
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: Compare a cone with its matching cylinder
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