The lengths of the edges of a cube are increasing at a rate of 4 ft/min.At what rate is the surface area changing when the edges are 21 ft long? A) 96 ft²/min B) 1,008 ft²/min C) 504 ft²/min D) 2,016 ft²/min E) 84 ft²/min

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Quizplus · Accepted Answer

The surface area of a cube is given by $6s^2$, where $s$ is the length of an edge. The rate of change of the surface area with respect to time, $dA/dt$, can be found by differentiating the area formula with respect to time: $dA/dt = 12s(ds/dt)$. Given $ds/dt = 4$ ft/min and $s = 21$ ft, substituting these values gives $dA/dt = 12 \times 21 \times 4 = 1008$ ft²/min.

​The Lengths of the Edges of a Cube Are Increasing

The Lengths of the Edges of a Cube Are Increasing