Question

Water is flowing into cylindrical tank of radius $7ft$ at the rate of $22c.ft/sec$. Then the rate of change in the water level is

• A. $7ft/sec$
• B. $\frac{1}{7}ft/sec$
• C. $\frac{2}{7}ft/sec$
• D. $\frac{7}{2}ft/sec$

Answer 1

Answer: (B)

$\frac{1}{7}ft/sec$

volume of the cylinder = $\pi (r{)}^{2}h$

$\frac{dv}{dt}=\pi (r{)}^2\frac{dh}{dt}$

$\frac{dv}{dt}=22c.ft/s$ $r=7ft$

$22=\frac{22}{7}\times 7\times 7\times \frac{dh}{dt}$

$\frac{dh}{dt}=\frac{1}{7}ft/sec$