Hello, Super Mallow!

3) Coffee is draining from a conical filter nto a cylindrical coffee pot at the rate of 10 in³/min.

a) How fast is the level in the pot rising when the coffee in the cone is 5 inches deep?

b) How fast is the level in the cone falling then?

[A diagram on the page shows the height and diameter of the cone is 6 inches;

diameter of pot is also 6 inches] Code:

: - 3 - : - 3 - :
- *-------+-------*
: \ | /
: \ | r / *---------------*
: \----+----/ | |
6 \:::|:::/ |-------+-------|
: \::|h:/ |:::::::|:::::::|
: \:|:/ |:::::::|:::::::|y
: \|/ |:::::::|:::::::|
- * *-------+-------*
: - 3 - : - 3 - :

(a) The pot has radius of 3 inches.

The coffee in the pot has radius 3 and height .

The volume of the coffee in the pot is: .

Hence, the volume of coffee is: .

Differentiate with respect to time: .

We are told that: in³/min.

So we have: .

The coffee in the pot is rising at a rate of about

(b) The cone has radius 3 and height 6.

The coffee in the cone has radius and height .

The volume of the coffee is: . .**[1]**

From the similar right triangles, we have: .

Substitute into [1]: .

Differentiate with respect to time: . .**[2]**

We are given: . in³/min

Substitute into [2]: .

The coffee in the cone is falling at about