Free Volumes of revolution questions for IB Mathematics: Applications & Interpretation (SL & HL), HL only, part of Calculus. Each question has the answer and the marking points an examiner would look for.
Generate a full Volumes of Revolution worksheet →All Calculus questionsThe region enclosed by the graph of y = 3x + 1, the x-axis and the lines x = 1 and x = 5 is rotated through 360° about the x-axis.
Find the volume of the solid formed.
| Part | Answer and marking points | Marks |
|---|---|---|
| 9.42 V = π∫y2dx (M1) correct integrand and limits (A1)(A1) 9.42 A1 | 4 |
The region enclosed by the graph of y = 3x + 1, the x-axis and the lines x = 1 and x = 3 is rotated through 360° about the x-axis.
Find the volume of the solid formed.
| Part | Answer and marking points | Marks |
|---|---|---|
| 7.07 V = π∫y2dx (M1) correct integrand and limits (A1)(A1) 7.07 A1 | 4 |
The region enclosed by the graph of y = 2 + sin x, the x-axis and the lines x = 0 and x = 4 is rotated through 360° about the x-axis.
Find the volume of the solid formed.
| Part | Answer and marking points | Marks |
|---|---|---|
| 76.6 V = π∫y2dx (M1) correct integrand and limits (A1)(A1) 76.6 A1 | 4 |
The region enclosed by the graph of y = 3x + 1, the x-axis and the lines x = 0 and x = 3 is rotated through 360° about the x-axis.
Find the volume of the solid formed.
| Part | Answer and marking points | Marks |
|---|---|---|
| 21.2 V = π∫y2dx (M1) correct integrand and limits (A1)(A1) 21.2 A1 | 4 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in