Grade 8 · Accumulate circular cross-sections · 490 of 750
Accumulate circular cross-sections · practice 54
Find the volume of a cylinder with radius 5.5 and height 6. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Find the volume of a cylinder with radius 5.5 and height 6.
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
The base is a circle, so find πr² before multiplying by height.
Work through the reasoning
Step 1
Translate the givens
The circular base area is π × 5.5² = 30.25π square units; 5.5 is the radius, not the diameter.
Step 2
Calculate with the model
Volume = base area × height = 30.25π × 6 = 181.5π.
Step 3
Check and interpret
Numerically this is approximately 570.19907 cubic units. Dividing the exact volume by height 6 recovers the base area 30.25π.
The answer
181.5π ≈ 570.19907 cubic units.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
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. Starting quantities: Base radius = 5.5; Cylinder height = 6.
V = πr²h
03 · Reflect and transfer
Explain what changes and why.
Why does doubling the radius multiply volume by four while doubling height only doubles it?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.