Question

the dimensions of a conical funnel are shown below. lolita 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 12 cubic inches per minute, how long will it take for all the liquid to pass through the nozzle? (use π = 3.14.) 3.14 minutes 9.42 minutes 2.09 minutes 4.19 minutes

Explanation:

Step1: Calculate volume of cone

The volume formula for a cone is $V=\frac{1}{3}\pi r^{2}h$. Given $r = 4$ inches and $h=3$ inches, and $\pi = 3.14$. So $V=\frac{1}{3}\times3.14\times4^{2}\times3$.
$V=\frac{1}{3}\times3.14\times16\times3=50.24$ cubic - inches.

Step2: Calculate time

The liquid drips at a rate of 12 cubic inches per minute. Let $t$ be the time in minutes. We know that rate $\times$ time = volume, so $t=\frac{V}{rate}$. Substituting $V = 50.24$ cubic inches and rate = 12 cubic inches per minute, we get $t=\frac{50.24}{12}\approx4.19$ minutes.

Answer:

4.19 minutes