Question

A cone of radius 2 cm and height 5 cm is lowered point first into a tall cylinder of radius 7 cm that is partially filled with water. Determine how fast the depth of the water is changing at the moment when the cone is completely submerged if the cone is moving with a speed of 3 cm/s at that moment.

Answer 1

adding $\pi 2^2$ both side

$\pi 2^2=\pi 7^2*\frac{dX}{dt}$

divide both side by : $\pi 7^2$

$\frac{2^2}{7^2}=\frac{dX}{dt}$

thus change in water level with time is $\frac{4}{49}\frac{cm}{sec}$