Unit 5: Calculus
Topic 5.17: Volumes of revolution (HL only) Questions
Practice 20 exam-style questions for IB Math AA SL Topic 5.17. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
Rotating about the x-axis, the disc at position x has radius:
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The region under y = 3, from x = 1 to x = 5, is rotated 360° about the x-axis. Find the exact volume, and say what solid it is.
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2026
The area between a curve and the y-axis is given by:
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The curve x = g(y) passes through points giving x = 2y + 1. Find the area between this curve and the y-axis from y = 0 to y = 3.
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2026
To set up ∫ x dy for the curve y = x⁵ (x ≥ 0), x =
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A volume-of-revolution answer of 12 (no π) most likely means the student:
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For a region between two curves rotated about an axis, you compute:
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2026
The area between y = ln x and the y-axis from y = 0 to y = 1 is:
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The curve y = x³ (x ≥ 0) and the y-axis enclose a region between y = 0 and y = 8. Find the exact area.
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2026
A region is bounded by y = √x (x ≥ 0), the y-axis, x = 0 and x = 4. Using horizontal strips, find the area between the curve and the y-axis.
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For ∫ x dy with x = y² between y = 1 and y = 2, the value is:
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If you're given x-limits but integrate x dy, you must:
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The region under y = 2x, from x = 0 to x = 3, is rotated 360° about the x-axis. Find the exact volume.
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2026
y = √x rotated about the x-axis from x = 0 to 9 gives volume:
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2026
To rotate y = x³ about the y-axis you first write:
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Show that the volume generated is .
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The region between y = √x (outer) and y = x² (inner), from x = 0 to x = 1, is rotated 360° about the x-axis. Find the exact volume.
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Find the volume generated, giving an exact answer.
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2026
The curve y = ln x, the x-axis, and x = e bound a region. It is rotated 360° about the y-axis. Show the volume can be written as an integral, and find it (to 3 s.f.).
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2026
The region bounded by y = eˣ, the y-axis, and the lines y = 1 and y = 4 is measured against the y-axis. Find the exact area.
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