# Calculus

posted by .

Water is being pumped into an inverted conical tank at a constant rate. The tank has height 9 meters and the diameter at the top is 4 meters. If the water level is rising at a rate of 28 centimeters per minute when the height of the water is 3.5 meters, find the rate at which water is being pumped into the tank in cubic centimeters per minute.

I got it down to pi/4 * (4/9)^2 *(350)^2 * 28 = 532131.4956 but it's not right. Any suggestions?

• Calculus -

let the height of the water be h cm
let the radius of the water level be r cm
by similar triangles, r/h = 2/9 , r = 2h/9

V = (1/3)pi(r^2)h
= (1/3)pi(4/81)(h^2)h = (4pi/243)h^3
dV/dt = (4pi/81)(h^2)dh/dt
= (4pi/81)(350)(28) = 1520.375 cm^3/min

check my calculations

• oops - Calculus -

I did it again!

forgot to square the 350 in the last line

(4pi/81)(350)^2(28) = 532131.4964 cm^3/min

MMMHHHH ?

• Calculus -

What the heck? haha.

I was going crazy could I could've swore I did my calculations right. Oh well, thanks for the help man. I appreciate it.

## Similar Questions

1. ### calculus

Water is leaking out of an inverted conical tank at a rate of 60000 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 90 meters and the diameter at the top is …
2. ### Calculus

Water is leaking out of an inverted conical tank at a rate of 1100.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top …
3. ### Calculus

Water is leaking out of an inverted conical tank at a rate of 1100.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top …
4. ### Calculus (pleas help!!!)

Water is leaking out of an inverted conical tank at a rate of 1100.0 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 15.0 meters and the diameter at the top …

Water is leaking out of an inverted conical tank at a rate of 13200 cubic centimeters per min at the same time that water is being pumped into the tank at a constant rate. The tank has height 9 meters and the diameter at the top is …
6. ### Calculus

Water is leaking out of an inverted right conical tank at a rate of 0.0115 m^3/min. At the same time water is being pumped into the tank at a constant rate. The tank has height 11 meters and the diameter at the top is 7 meters. If …
7. ### Math

Water is leaking out of an inverted conical tank at a rate of 0.0109 {\rm m}^3{\rm /min}. At the same time water is being pumped into the tank at a constant rate. The tank has height 9 meters and the diameter at the top is 4.5 meters. …
8. ### Math

Water is leaking out of an inverted conical tank at a rate of 0.0109 {\rm m}^3{\rm /min}. At the same time water is being pumped into the tank at a constant rate. The tank has height 9 meters and the diameter at the top is 4.5 meters. …
9. ### Math

Water is leaking out of an inverted conical tank at a rate of 0.0109 {\rm m}^3{\rm /min}. At the same time water is being pumped into the tank at a constant rate. The tank has height 9 meters and the diameter at the top is 4.5 meters. …
10. ### Calculus

Water is leaking out of an inverted conical tank at a rate of 0.0142 m3/min. At the same time water is being pumped into the tank at a constant rate. The tank has height 13 meters and the diameter at the top is 3.5 meters. If the water …

More Similar Questions