An ice block is melting so that the length of each side is changing at the rate of 1.5 inches per hour. How fast is the surface area of the ice cube changing at the instant the ice block has a side length of 2 inches?

d SA / dt = 36 in ^2 / hour

Step-by-step explanation:

Surface area of a cube is 6s^2

We need to take the derivative with respect to t

d SA / dt = ds / dt * 12 s

We know ds / dt is 1.5 inches per hour

s = 2 for the particular instant we are looking at

d SA / dt = 1.5 * 12 * 2

d SA / dt = 36 in ^2 / hour