waecmaths question:
Water flows out of a pipe at a rate of 40πcm3 per second into an empty cylindrical container of base radius 4cm. Find the height of water in the container after 4 seconds
Option A:
10cm
Option B:
14cm
Option C:
16cm
Option D:
20cm
waecmaths solution:
$\begin{align} & Given\text{:} \\ & \frac{dV}{dt}=40\pi c{{m}^{3}}/s \\ & r=4cm\text{ } \\ & t=4\operatorname{s}. \\ & V=\pi {{r}^{2}}h=\pi ({{4}^{2}})h=16\pi h \\ & \frac{change\text{ }in\text{ }volume}{change\text{ }in\text{ }time}=\frac{dV}{dt} \\ & \frac{16\pi h}{4}c{{m}^{2}}/s=40\pi c{{m}^{3}}/s \\ & h=\frac{40\times 4}{16}cm=10cm \\\end{align}$
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