Water is flowing into an inverted upright cone with fixed height $H$cm and fixed radius $R$cm (as sh

Question

Water is flowing into an inverted upright cone with fixed height $H$cm and fixed radius $R$cm (as shown in the diagram) such that the radius of the surface of the water is increasing at a constant rate of $k$cm s$^{-1}$. Find, in terms of $H$ and / or $R$, the rate of change of the curved surface area of the cone that is in contact with the water when the cone is filled to $\frac{1}{8}$ of its capacity. In the diagram, the angle $	heta $ subtended by a minor circular arc $AB$ of fixed radius $5$cm is increasing at a constant rate of $\alpha $ rad s$^{-1}$. Find the rates of change of the area of the minor segment $ACB$ at the instants when the area of triangle $OAB$ is $7.5$ cm$^{2}$.

Accepted Answer

(a) $\pi k\sqrt{R^2 + H^2}$ (b) $\dfrac{5}{2}\alpha$ or $\dfrac{45}{2}\alpha$

Applications of Differentiation Q1

Applications of Differentiation Q1

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