| Exam Board | OCR |
|---|---|
| Module | C4 (Core Mathematics 4) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Volumes of Revolution |
| Type | Volume with trigonometric functions |
| Difficulty | Standard +0.8 This question requires setting up and evaluating a volume of revolution integral with trigonometric functions including cosec x, expanding (2sin x + cosec x)², integrating terms involving sin²x and cosec²x, and applying trigonometric identities. The algebraic manipulation and integration steps are non-trivial, and arriving at the exact form requires careful work, making it moderately harder than average C4 questions. |
| Spec | 4.08d Volumes of revolution: about x and y axes |
3.
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The diagram shows the curve with equation $y = 2 \sin x + \operatorname { cosec } x , 0 < x < \pi$.\\
The shaded region bounded by the curve, the $x$-axis and the lines $x = \frac { \pi } { 6 }$ and $x = \frac { \pi } { 2 }$ is rotated through four right angles about the $x$-axis.
Show that the volume of the solid formed is $\frac { 1 } { 2 } \pi ( 4 \pi + 3 \sqrt { 3 } )$.\\
\hfill \mbox{\textit{OCR C4 Q3 [7]}}