Q. 28 - Calculus

Question

The work required to pump all of the water out of a cylinder with radius 3.5 feet and depth 4 feet. 

Step-by-Step Solution

Answer

$Work done=\frac{A\rho H^2}{2}J$

Step1. Given Information

radius=3.5feet

depth=4feet

Step2. Calculate

$$\begin{gathered} dV=Adh \\ dW=\rho hdV \\ Integrating both side with proper limits and substituting the value of dV. \\ W={\int }_0^H\rho hAdh \\ W=\rho A\frac{h^2}{2}{|}^H \\ W=\frac{A\rho H^2}{2} J \end{gathered}$$