A right circular conical funnel has total height 30 cm and top radius 10 cm
MATHEMATICS · Multi-part · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives
Problem
A right circular conical funnel has total height 30 cm and top radius 10 cm. Initially, the funnel is full of water. Water drains through a small hole at the tip at a constant rate of 15 cm3/s.
Let h(t) be the water depth (in centimeters) at time t seconds.
(a) Obtain an equation expressing the volume of water in the funnel as a function of h.
(b) Find the instantaneous rate of change dtdh when the water depth is 12 cm. State the answer with units.
(c) Determine how fast the radius of the water surface is changing, dtdr, at the same instant.