Unit 5: Calculus
Topic 5.12: Areas & volumes of revolution (HL only) Questions
Practice 20 exam-style questions for IB Math AI SL Topic 5.12. Review the question stems below, then unlock the full Question Bank to access markschemes, model answers, and AI grading.
11 mark
2026
To find the area between y = f(x) (upper) and y = g(x) (lower) you integrate:
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Rotation about the y-axis uses the formula:
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The line y = 2x for 0 ≤ x ≤ 3 is rotated about the x-axis. Find the volume.
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The area under y = f(x) from x = 2 to x = 5 (f above the axis) equals:
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Before integrating for a volume of revolution about the x-axis, you must:
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A solid of revolution formed from a curve measured in cm has a volume measured in:
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The limits for an 'area between two curves' question are usually:
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If part of a curve dips below the x-axis, a single plain integral over the whole region gives:
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The line y = 2x for 0 ≤ x ≤ 3 rotated about the x-axis gives volume:
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The line y = 2x for 0 ≤ y ≤ 4 is rotated about the y-axis. Find the volume.
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The curve y = x² for 0 ≤ x ≤ 2 is rotated about the x-axis. Find the volume.
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The region under y = x² for 0 ≤ x ≤ √3 is rotated about the y-axis. Find the volume.
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The curve y = eˣ for 0 ≤ x ≤ 1 is rotated about the x-axis. Find the volume to 3 s.f.
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The curve y = x² for 0 ≤ x ≤ 2 rotated about the x-axis gives volume:
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A vase is modelled by rotating y = √x for 0 ≤ x ≤ 9 about the x-axis (cm).
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Find the area enclosed between them.
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To find the area between a curve and the y-axis you integrate:
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A path's edge follows y = 2 + 0.1x² for 0 ≤ x ≤ 6 (metres), the other edge along the x-axis. Find the area of the region.
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Find the area enclosed between y = x² and y = 2x.
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