A weather balloon is photographed from above so that it appears as a circle whose…
MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A weather balloon is photographed from above so that it appears as a circle whose circumference is increasing at a constant rate of 4cm/s. When the circumference reaches 80cm, answer the following:
(a) Determine the instantaneous rate at which the radius is changing.
(b) Hence find the rate at which the area enclosed by the circumference is changing at that instant.
(c) If the circumference was 60cm when the observation began, calculate the time taken (in seconds) for the circumference to grow to 80cm.