The curve $C$ has equation $x^2 - y^2 = 16$, where $y \geq 0$. The line $L$ has equatio

Question

The curve $C$ has equation $x^2 - y^2 = 16$, where $y \geq 0$. The line $L$ has equation $y = -\frac{1}{2}x + \frac{11}{2}$. Find the area enclosed by $C$, $L$ and the line $x = 8$.[3] For $x > 0$, the region bounded by $C$, $L$ and the $x$-axis is rotated about the $x$-axis through $2\pi$ radians. Find the exact volume generated. [4] The region bounded by $C$, the line $x = 5$ and the $x$-axis is rotated about the $y$-axis through $2\pi$ radians. Find the exact volume generated. [4]

Accepted Answer

(a) $8.47\text{ units}^2$ (b) $\dfrac{67\pi}{3}\text{ units}^3$ (c) $18\pi\text{ units}^3$

2025 NYJC P1 Q11

2025 NYJC P1 Q11

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