Water is poured at $36\, ext{m}^3/ ext{s}$ into a cylindrical vessel…

Question

Water is poured at $36\,	ext{m}^3/	ext{s}$ into a cylindrical vessel of base radius 3 m. The rate at which water level rises is:

Accepted 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.

Answer

1 m/s

Answer

$36\pi$ m/s

Answer

$9\pi$ m/s

Water 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: