| Exam Board | CAIE |
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| Module | FP1 (Further Pure Mathematics 1) |
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| Year | 2004 |
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| Session | November |
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| Topic | Parametric equations |
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2 The curve \(C\) is defined parametrically by
$$x = a \cos ^ { 3 } t , \quad y = a \sin ^ { 3 } t , \quad 0 \leqslant t \leqslant \frac { 1 } { 2 } \pi$$
where \(a\) is a positive constant. Find the area of the surface generated when \(C\) is rotated through one complete revolution about the \(x\)-axis.