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 compare a cone with its matching cylinder.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Cylinder volume and fractions.
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 cone and cylinder both have radius 4 cm and perpendicular height 9 cm. Find each volume and the amount of volume between them.
Why this math matters
A cone has one third of the volume of a cylinder with the same base area and perpendicular height. Use a matching simple reference solid to remember the cone's volume factor.
Set up the model
A useful answer starts with clear assumptions:
- The solids share the stated base radius and perpendicular height.
- Use geometric volume with no wall thickness.
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.
Compare a cone with its matching cylinder
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A cone and cylinder both have radius 4 cm and perpendicular height 9 cm. Find each volume and the amount of volume between them.
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
cylinder volume = π(4²)(9) = 144π cm³
First compute the volume of the matching constant-cross-section solid.
Apply the relationship
cone volume = (1/3)(144π) = 48π cm³
The cone occupies one third of that reference volume.
Check and interpret
difference = 144π − 48π = 96π cm³
The missing portion is two thirds of the cylinder volume.
The result
difference = 144π − 48π = 96π cm³
The missing portion is two thirds of the cylinder volume.
Common mistakes to catch
- Use perpendicular height rather than the cone's slant height in the volume formula.
- The one-third comparison requires both the same base area and the same height.
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 a cone's volume when radius is 3 m and perpendicular height is 5 m.
Show a hint
Use one third of πr²h.
Reveal answer and explanation
15π m³
(1/3)π(9)(5) = 15π.
Practice 2
A cone and cylinder share a base and height. If the cone holds 18 units³, what is the cylinder's volume?
Show a hint
Reverse the one-third relationship.
Reveal answer and explanation
54 units³
The cylinder volume is 3 × 18 = 54.
Take the idea with you
Use a matching simple reference solid to remember the cone's volume 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: Connect sphere volume to cubic scaling
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