Question

Water is stirred inside a beaker to form a parabolic surface. Given that the volume of the parabolic shape generated inside is V = pi (3h^2 + 10h), where h is the height of the parabola in mm. Find the rate of change of volume, V when the rate of change of height, h is 2 mm per second, at the moment when the height of parabola is 8mm.

Answer 1

You know how the volume varies with height, and the time rate of change of the height h at height of 8mm. You can apply rules of related rates, basically that\[\frac{dV}{dt} = \frac{dV}{dh}\frac{dh}{dt}.\] You can find dV/dh by taking the derivative and plugging in the known value of h, and you know dh/dt. Multiply, and dV/dt falls out.

Answer 2

thank u so much. i did it X)