A bowl is created with circular cross sections so that its radius (in cm) is a function of height (in cm) according to the equation r=4sqrt(h+1). Find the volume of soup that fills the bowl if the bow is 2 cm high.

Answer 1

Consider the interior of the bowl as a stack of thin circles. At height h, the circle has area

πr^2 = π(16(h+1))

So integrate that from 0 to 2