A spherical balloon is being inflated so that its radius changes with time

MATHEMATICS · Multi-part · A Level · Mathematics · Differentiation · Differentiation

Problem

A spherical balloon is being inflated so that its radius rr changes with time tt. The surface area of a sphere is S=4πr2S=4\pi r^{2}. (a) Write an expression for dSdt\dfrac{dS}{dt} in terms of rr and drdt\dfrac{dr}{dt}. Do not substitute numerical values. (b) Describe, in complete sentences, how a change in the radius affects the instantaneous rate of change of the surface area. Reference the mathematical relationship from part (a). (c) Suppose the radius is increasing at a constant rate. Explain whether dSdt\dfrac{dS}{dt} is also constant. Justify your answer verbally and algebraically.

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