00:01
So we have a cube and the volume of a cube is side cubed, where s is the side length.
00:11
Now we're told the volume is decreasing, so we have dv dt and that is going to be 2604, so negative 2604 cubic meters per second.
00:28
At the instant when the volume is 951, what's the rate of change of the surface area? so i want da dt and i want that when volume equals 951.
00:48
Okay, so i'm going to start with my volume formula and if i take the derivative of that, i have 1 dv dt equal to 3s squared ds dt.
01:03
I know that dv dt is negative 2604 and i'm just going to hold up for one minute.
01:17
When my volume is 951, i'm going to get the side length, so i'm going to get an s of 9 .83392, so i'm going to plug that in.
01:59
That gives me negative 2604 equal to 290 .1181722 ds dt.
02:11
Divide both sides and ds dt is equal to 8 .975653...