Unit 5: Calculus
Topic 5.17: Areas and 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.
1Find2 marks
2026
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
A volume-of-revolution answer of 12 (no π) most likely means the student:
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2026
For a region between two curves rotated about an axis, you compute:
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2026
The area between a curve and the y-axis is given by:
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2026
Rotating about the x-axis, the disc at position x has radius:
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2026
To set up ∫ x dy for the curve y = x⁵ (x ≥ 0), x =
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2026
The line x = 2y + 1 is drawn for 0 ≤ y ≤ 3. Find the area between this line and the y-axis from y = 0 to y = 3.
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2021
The volume of a solid of revolution is cm, where . Given that cm, find .
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2022
A vase holds m of water when filled to a height of m. Water flows in at m s. Find the time taken to fill it to a height of m.
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2026
y = √x rotated about the x-axis from x = 0 to 9 gives volume:
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2026
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
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 the curve y = √x, the y-axis and the line y = 2. Using horizontal strips, find the area of the region.
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2026
To rotate y = x³ about the y-axis you first write:
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2022
The region under from to is rotated about the -axis. Show that the volume generated is .
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2026
For ∫ x dy with x = y² between y = 1 and y = 2, the value is:
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2026
If you're given x-limits but integrate x dy, you must:
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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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2024
The region under from to is rotated about the -axis. Find the exact volume generated.
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2022
A vase is modelled by rotating the curve , for , through about the -axis. Show that the volume up to a height is .
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