Question

Coffee is draining from a conical filter into a cylindrical coffee pot at the rate of 10 in^3/min. How fast is the level of the pot rising when the coffee in the cone is 5 in. deep. Also, How fast is the level in the cone falling then?
Height of cone is 6 inches, diameter of cone is 6 inches and diameter of cylinder is 6 inches too. Please is the answer to the first question 30Pi?

Answer 1

What um... What subject is this?

Answer 2

Math @MaydayPaRAYde

Answer 3

Yes... But... Like Watch TYPE of math?

Answer 4

It's Calclus..related rates (rate of change)

Answer 5

Oh Okay! I'll work on it

Answer 6

Yay!...thank you so much!

Answer 7

part A is 10/(9 pi).
r = 3 for the cone.

Answer 8

yope!...10/9pi?...how though?

Answer 9

A.) Diameter of Pot, d = 6 in.
Volume = V
dV/dt = 10 cu. in./min.
Level of Pot = h

Find dh/dt:

V = π r² h
V = π (d² / 4) h
V = π [(6)² / 4] h
V = π (36 / 4) h
V = π (9) h
V = 9π h
V = 28.27h

Differentiating Implicitly Over Time:

dV/dt = 28.27(dh/dt)
10 = 28.27(dh/dt)
dh/dt = 10 / 28.27
dh/dt = 0.354

The level of the pot is increasing at a rate of 0.354 in./min.

(Since the change in volume is the same notwithstanding the sign, the level in the filter makes no difference)

Answer 10

Hope this was helpful :3 Is there anything else?

Answer 11

Isn't the volume of a cone 1/3*pi*r^2h

Answer 12

B.) Diameter of Cone, d = 6 in.
Height of Cone, h = 6 in.
Volume of Cone = V
dVc/dt = - 10 cu. in./min.

Find dh/dt:

V = 1/3 π r² h
V = 1/3 π (d / 2)²h
V = 1/3 π (d² / 4)h
V = 1/3 π [(6)² / 4)h
V = 1/3 π (36 / 4)h
V = 2/3 π (9)h
V = 18/3 π h
V = 6π h
V = 18.85h

Differentiating:

dV/dt = 18.85(dh/dt)
- 10 = 18.85(dh/dt)
dh/dt = - 10 / 18.85
dh/dt = - 0.531

The level of the cone is decreasing at a rate of 0.531 in./min.

Yes ^-^

Answer 13

hmm...Thank you very much! :-D

Answer 14

_•)
<) )╯ 'where did my other eye go'
/ \
(•_•)
<( (> 'there it is lol'
/ \

Answer 15

You're Welcome :DD sorry it took me so long I didn't see your question.

Answer 16

LOL!!!...

Answer 17

It's aiit...glad you eventually helped!

Answer 18

Aha You're welcome :)

Answer 19

I have found a little problem with your solution @MaydayPaRAYde the question said in part A, that we should find dh/dt when h = 5 inches

Answer 20

or was it just put to confuse us...just like they gave us the height of the cone? @MaydayPaRAYde

Answer 21

Maybe I'm just confusing myself