The total surface area of a cone with radius and height is given by

MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

The total surface area of a cone with radius rr and height hh is given by S=πr2+πrr2+h2S = \pi r^2 + \pi r \sqrt{r^2 + h^2} . A cone has height 5 cm and the radius increases at the rate of 2 cm per second. Find the rate at which the surface area is increasing when the radius equals 10 cm.

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