The surface area of a cube with edge length is

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

Problem

The surface area

S

of a cube with edge length

a

S=6a^{2}

. During an experiment, the edge is increasing at

1.5\,\text{cm/s}

while the surface area is increasing at

108\,\text{cm}^{2}/\text{s}

. What is the edge length

a

(in cm) at that instant? (a)

12

(b)

9

(c)

6

(d)

5