Question

Surface Area: All edges of a cube are expanding at a rate of 6 centimeters per second. How fast is the surface area changing when each edge is (A) 2 centimeters and (B) 10 centimeters?

Answer 1

Given: de/dt where e= length of an edge and t= time, find da/dt where a= surface area.

Answer 2

We know that da/dt = de/dt * da/de

Answer 3

The equation of surface area for a cube is \[e^{2}*6=a\]

Answer 4

Once finding da/de for the above equation, plug it into the first equation with with the given values and you should be able to solve for da/dt :)

Answer 5

Thank you. I utilized the given information along with your explanation, and received the following answers by working out the word problem. I hope the answers are correct.
\[Part A: \frac{ da }{ dt }(2) = (12)(6)(2) = 144cm ^{3}/\sec\]
\[Part B: \frac{ da }{ dt }(10) = (12)(6)(10) = 720cm ^{3}/\sec\]

Answer 6

One second, I'll check them.

Answer 7

Yes that matches with what I got. :) Good job.

Answer 8

Thank you!! :)