BitWithBite
Mathematics Worksheet
🧊 Volumes
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Use the disk method to find volumes of revolution.Set up V = π ∫ [f(x)]2 dx.Evaluate volume integrals.Match the integration variable to the axis of rotation.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Disk method: V = ?
2Rotating f(x) = x on [0, 4] gives volume:
3Rotating f(x) = 3 on [0, 2] gives volume:
4Rotating f(x) = x2 on [0, 1] gives volume:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Disk method: V = .
6Rotating f(x) = x on [0, 4] gives V = .
7Find the volume rotating f(x) = x on [0, 4] (disk method).
8Find the volume rotating f(x) = 3 on [0, 2] (disk method).
9Find the volume rotating f(x) = √x on [0, 9] (disk method).
🚀 Section C · Challenge ● CHALLENGE 5
10Find the volume rotating f(x) = x2 on [0, 1] (disk method).
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-B 3-B 4-B | 5 π ∫ [f(x)]2 dx 6 64π/3 7 = 64π/3 8 = 18π 9 = 81π/2 | 10 = π/5