Question

The dimensions of a conical funnel are shown below:

A conical funnel is shown with the height of the cone as 6 inches and the radius of the base as 2 inches.

Nadia closes the nozzle of the funnel and fills it completely with a liquid. She then opens the nozzle. If the liquid drips at the rate of 10 cubic inches per minute, how long will it take for all the liquid to pass through the nozzle? (Use π = 3.14.)
2.51 minutes
7.53 minutes
4.18 minutes
3.14 minutes

Answer 1

2.51 minutes

Explanation:

Step 1: Find the total volume of the funnel

The volume of a cone can be calculated by below formula:

`V=(1)/(3)pi*r^(2)h`

Where V is volume, pi is π, r is the radius of the base of the cone and h is the height of the cone

pi = 3.14

r = 2 inches

h = 6 inches

`V=(1)/(3)pi*r^(2)h`

`V=(1)/(3)*3.14*2^(2)*6`

`V=25.12 in^(3)`

Step 2: Determine the time taken for funnel to empty

Assuming rate of emptying of funnel is constant

`t=(V)/(R)`

Where t is the time taken to empty the funnel and R is the rate at which the liquid drips

V = 25.12 cubic inches

R = 10 cubic inches/minute

`t=(V)/(R)`

`t=(25.12)/(10)`

`t=2.512 minutes`

Answer 2

Volume of a conical funnel = π r² h/3
v = 3.14 * (2in)² * 6in/3
v = 3.14 * 4in² * 2in
v = 25.12 in³

25.12 in³ ÷ 10 in³ per minute = 2.512 minutes

It will take 2.51 minutes for all the liquid to pass through the nozzle.