# Thread: related rates prob: how fast is the surface area increasing?

1. ## related rates prob: how fast is the surface area increasing?

I am doing a related rates problem and I have no idea how to set it up. I haven't been able to find any examples in my book, notes or web on this one. I need help setting this up.

"The volume of a cube is increasing at a rate of 10cm^3 per minute. How fast is the surface area increasing when the length of an edge is 30 cm."

Any help as soon as possible would greatly be appreciated.

2. The volume of a cube is increasing at a rate of 10cm^3 per minute
dV/dt = 10 cm<sup>3</sup>/min

How fast is the surface area increasing when the length of an edge is 30 cm.?
they want dA/dt when s = 30 cm

equations needed ...
volume of a cube, V = s<sup>3</sup>
surface area of a cube, A = 6s<sup>2</sup>

d/dt[A = 6s<sup>2</sup>]
dA/dt = 12s(ds/st)
to find dA/dt ... you have s, but need the value of ds/dt.

d/dt[V = s<sup>3</sup>]
dV/dt = 3s<sup>2</sup>(ds/dt)
you have dV/dt and s ... you can solve for ds/dt, then you can determine dA/dt.

3. thanks that really helps! I am so glad you replied quickly.

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•