Answer:
a) Depth changing rate of change is
, When the water is 6 meters deep
b) The width of the top of the water is changing at a rate of
, When the water is 6 meters deep
Step-by-step explanation:
As we can see in the attachment part II, there are similar triangles, so we have the following relation between them
, then
.
a) As we have that volume is
, then
, so we can derivate it
due to the chain rule, then we clean this expression for
and compute with the knowns
, is the depth changing rate of change when the water is 6 meters deep.
b) As the width of the top is
, we can derivate it and obtain
The width of the top of the water is changing, When the water is 6 meters deep at this rate