A right circular cylinder has constant volume

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A right circular cylinder has constant volume 2000π cm32000\pi\text{ cm}^{3}. Its radius rr is increasing at a constant rate of 0.50 cm/s, and the height adjusts so that the volume constraint is maintained. At what radius will the surface area of the cylinder (including its top and bottom) stop increasing? (a) 15 cm15\text{ cm} (b) 10 cm10\text{ cm} (c) 7 cm7\text{ cm} (d) 20 cm20\text{ cm}

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