The curve $C$ has equation $y=\frac{\sqrt{x}}{{{(16-{{x}^{2}})}^{\frac{1}{4}}}},\,0\le xSketch $C$.

Question

The curve $C$ has equation $y=\frac{\sqrt{x}}{{{(16-{{x}^{2}})}^{\frac{1}{4}}}},\,0\le xSketch $C$. [2] Find the exact volume of revolution when the region bounded by $C$, the line $x=2\sqrt{3}$ and the $x$-axis, is rotated $2\pi $ radians about the $x$-axis. [4] A horizontal line $l$ intersects $C$ at $x=2\sqrt{3}$. Find the exact volume of revolution when the region bounded by $C$, the horizontal line $l$ and the line $x=0$, is rotated $2\pi $ radians about the $x$-axis. [2]

Accepted Answer

(ii) $2\pi\text{ units}^3$; (iii) $4\pi\text{ units}^3$

2019 TMJC Promo Q3

2019 TMJC Promo Q3

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