Calculating Constant Volume Rate of Change

[Stanc]

Homework Statement

A rectangular object has a fixed length of 1m. The height is increasing by 12 cm/min. Find the rate that the width must change so that the volume remains constant at 16 000cm^3 when the height is 10 cm

The Attempt at a Solution

So here's what I tried:

The Volume= Lenth x Width x Height
V = x y z Since x is fixed at 100 , V= 100 y z
dV/dt = 100y dz/dt +100 z dy/dt = 0
z dy/dt = -ydz/dt
(10) (12) = - y dz/dt
When x= 100 and z= 10 and V=16000 , y = 16
dz/dt = - (10)(12)/y = - 120/16 = -7.5 cm/min


However, I don't even know if I am taking the right approach... Please give me assistance

 

[Mark44]

Homework Statement

A rectangular object has a fixed length of 1m. The height is increasing by 12 cm/min. Find the rate that the width must change so that the volume remains constant at 16 000cm^3 when the height is 10 cm

The Attempt at a Solution

So here's what I tried:

The Volume= Lenth x Width x Height
V = x y z Since x is fixed at 100 , V= 100 y z
dV/dt = 100y dz/dt +100 z dy/dt = 0
z dy/dt = -ydz/dt
(10) (12) = - y dz/dt
When x= 100 and z= 10 and V=16000 , y = 16
dz/dt = - (10)(12)/y = - 120/16 = -7.5 cm/min


However, I don't even know if I am taking the right approach... Please give me assistance

Looks OK to me, but I didn't check that closely. It's reasonable to get a negative rate, since one dimension is increasing, and one is constant. It has to be true that the third dimension is decreasing, this you get a negative rate.

It would have been helpful to use variables that matched what they represent - h for height, and w for width. I have to do a bit of translation with y and z.

 

[Stanc]

Looks OK to me, but I didn't check that closely. It's reasonable to get a negative rate, since one dimension is increasing, and one is constant. It has to be true that the third dimension is decreasing, this you get a negative rate.

It would have been helpful to use variables that matched what they represent - h for height, and w for width. I have to do a bit of translation with y and z.

Ok sorry about the representation thing but is my approach correct? I just don't understand why I didnt have to use the chain rule...