Answer:
the drop in the level of water in the container is 2.03 cm
Step-by-step explanation:
The volume of a cylinder can be written as;
[tex]V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter[/tex]
the change in height when the volume changes can be derived by differentiating the equation.
[tex]dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}[/tex]
substituting the given values;
[tex]\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.[/tex]
[tex]dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm[/tex]
the drop in the level of water in the container is 2.03 cm
