## 101Ryan101 If the length of one a side of a cube is increasing at a rate of 4m/s how fast is the surface area of the cube increasing when the length is 16m. 2 years ago 2 years ago

1. pk51

This is related rates, right?

2. 101Ryan101

yea

3. beezlebub

768

4. pk51

I get 768 also. Hint. Relate the information, take a derivative, plug in what you know.

5. 101Ryan101

Oh thanks.. opps.

6. Alchemista

Its surface area not volume: $A = 6\cdot l^2$$\frac{dl}{dt} = 4$$\frac{dA}{dl} = 12 \cdot l \cdot \frac{dl}{dt}$$12 \cdot 16 \cdot 4 = 768$

7. 101Ryan101

so if I want to know the rate of increase of volume it's increasing much faster than the surface area so ... (I'm a bit confused as to taking the derivative of V here...) I know dL/dt = 4m/s so for volume...when the length is 16m V = L^3 dV/dt =(3L^2)dL/dt = (3)(16)^2)(4) = 3072m/s I assume that's correct. But I'm not used to seeing an extra dL/dt. I guess the explanation for that is that it's a dependent variable.