Free Volumes of revolution questions for IB Mathematics: Analysis & Approaches (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 R is enclosed by the curve y = 1x, the x-axis and the lines x = 1 and x = 3. R is rotated through 2π about the x-axis.
Find the exact volume of the solid formed.
| Part | Answer and marking points | Marks |
|---|---|---|
| 2π3 π∫1x2dx (M1) π[−1x] A1 π(1 − 13) A1 2π3 A1 | 4 |
The region enclosed by y = √x, the x-axis and x = 4 is rotated through 2π about the x-axis. Find the volume.
| Part | Answer and marking points | Marks |
|---|---|---|
| 25.1 π∫y2 dx (M1) correct integral (A1) 25.1 A1 | 3 |
The region R is enclosed by the curve y = ex, the coordinate axes and the line x = ln 2. R is rotated through 2π about the x-axis.
Find the exact volume of the solid formed.
| Part | Answer and marking points | Marks |
|---|---|---|
| 3π2 π∫e2xdx (M1) [πe2x2] A1 π2(4 − 1) A1 3π2 A1 | 4 |
The region enclosed by y = √x, the x-axis and x = 9 is rotated through 2π about the x-axis. Find the volume.
| Part | Answer and marking points | Marks |
|---|---|---|
| 127 π∫y2 dx (M1) correct integral (A1) 127 A1 | 3 |
The region R is enclosed by the curve y = √x, the x-axis and the line x = 2. R is rotated through 2π about the x-axis.
Find the exact volume of the solid formed.
| Part | Answer and marking points | Marks |
|---|---|---|
| 2π V = π∫y2dx (M1) π∫02x dx A1 π[x22]02 A1 2π A1 | 4 |
The region enclosed by y = 2√x, the x-axis and x = 9 is rotated through 2π about the x-axis. Find the volume.
| Part | Answer and marking points | Marks |
|---|---|---|
| 509 π∫y2 dx (M1) correct integral (A1) 509 A1 | 3 |
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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