alleryWater is poured at $36\,\text{m}^3/\text{s}$ into a cylindrical vessel of base radius 3 m. The rate at which water level rises is:
A1 m/s
B$\dfrac{36}{9\pi}$ m/s = $\dfrac{4}{\pi}$ m/s
C$36\pi$ m/s
D$9\pi$ m/s
Answer & Solution
Correct answer: B. $\dfrac{36}{9\pi}$ m/s = $\dfrac{4}{\pi}$ m/s
$V = \pi r^2 h$ (cylinder, $r$ constant).
$dV/dt = \pi r^2 \, dh/dt$ ⇒ $dh/dt = 36/(\pi \cdot 9) = 4/\pi$ m/s.
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