A cube has edge length at a certain instant

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

Problem

A cube has edge length 5 cm5\,\text{cm} at a certain instant. At that instant its volume is increasing at the rate of 60 cm3 ⁣ ⁣/s60\,\text{cm}^{3}\!\!{/}\text{s}. (a) Find the rate at which the edge length is changing at that instant. (b) If the rate found in part (a) remains constant, calculate the time required (in seconds) for the edge length to increase to 5.10 cm5.10\,\text{cm}.

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