Volumes of revolution
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Flip to reveal answersVolume of revolution about the x-axis?
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All 8 Flashcards — Volumes of revolution
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Question
Volume of revolution about the x-axis?
Answer
V = ∫ₐᵇ π y² dx — discs of radius y along x.
Question
Volume of revolution about the y-axis?
Answer
V = ∫꜀ᵈ π x² dy — discs of radius x; rewrite x² in terms of y, use y-limits.
Question
Why π·(radius)² in the integral?
Answer
Each thin slice is a disc; a disc's area is π·radius², and the volume sums the discs.
Question
Rotating about the y-axis: what must you change?
Answer
Express x² in terms of y AND switch the limits to the y-values.
Question
Volume of y = x² (0≤x≤2) rotated about the y-axis?
Answer
x² = y, y: 0→4, V = ∫₀⁴ πy dy = 8π ≈ 25.1.
Question
Volume between two curves rotated about the x-axis?
Answer
V = ∫ π(y_outer² − y_inner²) dx — subtract the inner disc.
Question
Common volume-of-revolution slip?
Answer
Forgetting to square the radius, dropping the π, or keeping x-limits on a y-axis solid.
Question
How does the GDC help with volumes of revolution?
Answer
Type the set-up integral ∫ π(radius)² and let it evaluate — a calculator is allowed on every AI paper.
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Full study notes for Volumes of revolution
Topic 5.12 hub
Areas & volumes of revolution (HL only)
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