OCR MEI C4 — Question 3 4 marks

Exam BoardOCR MEI
ModuleC4 (Core Mathematics 4)
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVolumes of Revolution
TypeRotation about x-axis: polynomial or root function
DifficultyModerate -0.3 This is a straightforward volume of revolution question requiring direct application of the formula V = π∫y²dx. Since y² = x-1 is already given, the integration is trivial (just ∫(x-1)dx), making this slightly easier than average with no algebraic manipulation or problem-solving required.
Spec4.08d Volumes of revolution: about x and y axes

3 The curve \(y ^ { 2 } = x - 1\) for \(1 \leq x \leq 3\) is rotated through \(360 ^ { \circ }\) about the \(x\)-axis. Find the volume of the solid formed.

Question 3:
AnswerMarks Guidance
Answer/WorkingMarks Guidance
\(V = \pi\int_0^2 y^2\, dx\)M1
\(= \pi\int_0^2 x^4\, dx = \pi\left[\frac{x^5}{5}\right]_0^2\)A1, A1
\(= \frac{32}{5}\pi\)A1
Total: 4 marks
## Question 3:

| Answer/Working | Marks | Guidance |
|---|---|---|
| $V = \pi\int_0^2 y^2\, dx$ | M1 | |
| $= \pi\int_0^2 x^4\, dx = \pi\left[\frac{x^5}{5}\right]_0^2$ | A1, A1 | |
| $= \frac{32}{5}\pi$ | A1 | |
| **Total: 4 marks** | | |

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3 The curve $y ^ { 2 } = x - 1$ for $1 \leq x \leq 3$ is rotated through $360 ^ { \circ }$ about the $x$-axis. Find the volume of the solid formed.

\hfill \mbox{\textit{OCR MEI C4  Q3 [4]}}