Question

A paper cup in the shape of an inverted cone has a diameter and a height of 4 inches. If water is leaking out of the cup at a rate of 1/2 cubic inches per second, how fast is the water level dropping when the diameter of the surface is 2 inches?

Answer 1

volume of a cone is found by taking a third of the product of its base area times its height.
When both the diameter and the height equal 4, we can find the volume by this equation: \[(((\frac{ D }{ 2 })^{2}\pi)h(1/3))\], where D means diameter and h means height.
So, the volume is \[\frac{ 1 }{ 3 }(4)(\frac{ 4 }{ 2 })^{2}\pi\] =\[\frac{ 16 }{ 3 }\pi\].

Answer 2

thank you!