Grade 8 · Volume
Community mural: Accumulate circular cross-sections
Community mural investigation: accumulate circular cross-sections. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
A cylinder accumulates identical circular cross-sections through its height. The base area is πr², so increasing radius affects volume quadratically while increasing height affects it linearly. Radius and diameter must be distinguished before squaring. This investigation begins with base radius = 6; cylinder height = 3.5. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
V = πr²h
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Read the radius of the circular base and use πr² to find its area.
- STEP 2
Follow the changing model
Playback raises the fill level through the cylinder, adding equal volumes for equal height increments.
- STEP 3
Check and explain the relationship
Multiply the base area by the full height. Compare doubling radius with doubling height to see the different scale effects.
Your turn to explain
Make a prediction. Test your reasoning.
Community mural: Find the cylinder volume for radius 6 and height 3.5.
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
126π ≈ 395.841 cubic units; the radius, not the diameter, is squared.
Work through a full lesson
Connect the animation to a worked example and practice questions.