The diagram shows a container that comprises of a cylinder and an inverted cone of radius $2.5$ cm

Question

The diagram shows a container that comprises of a cylinder and an inverted cone of radius $2.5$ cm, where the heights of the cylindrical part and the conical part are $20$ cm and $4$ cm, respectively. The container is initially full of water, and from $t = 0$, water flows out through a small hole at the vertex of the cone at a constant rate of $18$ cm$^3$ /s.

Let $x$ cm be the height and $r$ cm be the radius of the remaining water in the container after $t$ seconds.

Find the rate of change of $x$ when $x = 6$ cm.
Find the rate of change of $x$ when $x = 2$ cm.

Accepted Answer

(i) $-\dfrac{72}{25\pi}\text{ cm s}^{-1}$ (ii) $-\dfrac{288}{25\pi}\text{ cm s}^{-1}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

Solution:

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