Question

if 5 litres of water are drawn from a cylindrical container of internal diameter 56cm find the drop in the level of water in the container​

Answer 1

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;

$V = \pi r^2h=\frac{\pi d^2h}{4} \\where;\\r = radius \\h = height \\d = diameter$

the change in height when the volume changes can be derived by differentiating the equation.

$dV =\frac{\pi d^2}{4} dh\\dh = dV\frac{4}{\pi d^2}$

substituting the given values;

$\left \{ {{dV=5 litres= 5000cm^3} \atop {d=56 cm}} \right.$

$dh = 5000\frac{4}{\pi * 56^2}\\dh = 2.03cm$

the drop in the level of water in the container is 2.03 cm