RELATED RATES:
The volume of a cube is increasing at a rate of 10cm^3/min. How fast is the surface area increasing when the length of an edge is 30 cm?

Question

RELATED RATES:
The volume of a cube is increasing at a rate of 10cm^3/min. How fast is the surface area increasing when the length of an edge is 30 cm?

ipwnbunnies · Answer

I'll give you the plan, I don't have time to go through the entire problem unfortunately.
1. Find the volume of the cube when a side is 30cm. 
2. Derive the volume formula wrt t. You'll get dV/dt on the left. Find dside/dt, which is the rate of change of a side.
3. Get the surface area formula, find the derivative of it wrt t, so dSA/dt is on the left side.
4. Plug in your values for the sides and dside/dt, and solve for dSA/dt.

ipwnbunnies · Answer

dSA/dt should be in units of cm^2/min.

ayubie · Answer

thank you so much!