Hello, janedoe!
A conical tank is 12 ft across the top and 17 ft deep.
If water is flowing into the tank at a rate of 8 ft³/min,
find the rate of change of the depth when the water is 2 ft deep. Code:
: 6 :
- *-------+-------*
: \ | /
: \ | r /
: *----+----*
17 \ | /
: \ h| /
: \ | /
: \|/
- *
The volume of the water is: . .[1]
From the similar right triangles: .
Substitute into [1]: .
Differentiate with respect to time: .
Since . we have: .
. . Therefore: . ft/min.
And thank you, thank you for sharing your work and your thoughts!
You put in a lot of work before asking for help.
It is an extremely rare occurence . . .We truly appreciate it!