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 connect sphere volume to cubic scaling.
- Solve the two practice problems and explain how the assumptions affect the answers.
Before you start
Powers, fractions, and radius.
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 spherical model has radius 3 cm. Find its volume and the volume of a similar sphere with twice that radius.
Why this math matters
A sphere's volume is 4πr³/3, so changing its radius changes its volume by a cubic factor. Predict volume ratios from length ratios before calculating exact measurements of similar solids.
Set up the model
A useful answer starts with clear assumptions:
- Both objects are exact spheres.
- The given sizes are radii rather than diameters.
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.
Connect sphere volume to cubic scaling
PausedQuestion: Start with the question. Paused.
Question
Start with the question
A spherical model has radius 3 cm. Find its volume and the volume of a similar sphere with twice that radius.
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
V = (4/3)π(3³) = (4/3)π(27) = 36π cm³
Cube the radius before applying the factor 4π/3.
Apply the relationship
doubled radius = 6 cm; new V = (4/3)π(216) = 288π cm³
All three spatial dimensions scale by two.
Check and interpret
new/old = 288π/(36π) = 8
Doubling the radius multiplies volume by 2³, not by 2.
The result
new/old = 288π/(36π) = 8
Doubling the radius multiplies volume by 2³, not by 2.
Common mistakes to catch
- Squaring the radius belongs to area formulas, whereas sphere volume uses a cube.
- Doubling a diameter also doubles the radius, so the same cubic scale factor applies.
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 volume of a sphere with radius 2 m.
Show a hint
Use r³ = 8 in the sphere formula.
Reveal answer and explanation
32π/3 m³
(4/3)π(2³) = (4/3)π(8).
Practice 2
Two spheres have radius ratio 1:3. What is their volume ratio?
Show a hint
Cube the length ratio.
Reveal answer and explanation
1:27
The common 4π/3 factor cancels, leaving 1³:3³.
Take the idea with you
Predict volume ratios from length ratios before calculating exact measurements of similar solids.
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.
Completion is your own study record, not a test score. It stays in this browser, does not sync to another device, and can be removed by clearing browser data.