The diagram shows two sectors where $PQ$ and $MN$ are the arcs with centre $O$. \(OP = 2r

Question

The diagram shows two sectors where $PQ$ and $MN$ are the arcs with centre $O$. $OP = 2r$ cm, $PM = r$ cm and the perimeter of the sector $OMN$ is $90$ cm. Show that the area of the shaded region, $A$ cm$^2$, is given by $A = 75r - 5r^2$. Given that $A$ is increasing at a constant rate of $10$ cm$^2$/s, find the rate of change of $r$ when $r = 5$ cm.

Accepted Answer

(i) $A=75r-5r^2$ (ii) $\dfrac25\text{ cm s}^{-1}$

Differentiation - Connected Rates of Change

Differentiation - Connected Rates of Change

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