The lengths of the edges of a cube are increasing at a rate of 7 ft/min. At what rate is the surface area changing when the edges are 11 ft long? A) 588 ft²/min B) 924 ft²/min C) 1,452 ft²/min D) 294 ft²/min E) 3,234 ft²/min

Question

Quizplus · Accepted Answer

Let x be the length of an edge of the cube, and A be its surface area.
Then we have:
x' = 7 (the prime denotes differentiation with respect to time, t)
A = 6x^2
Differentiating both sides with respect to t, we get:
A' = 12x·x'
At the moment when x = 11, we have:
A = 6·11^2 = 726
x' = 7
So, A' = 12·11·7 = 924
Therefore, the surface area is increasing at a rate of 924 ft^2/min when the edges are 11 ft long.

The Lengths of the Edges of a Cube Are Increasing