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 $pi = 3.14$ )
4.19 minutes
2.09 minutes
5.42 minutes
3.14 minutes

Explanation:

Step1: Calculate funnel volume

The volume of a cone is $V=\frac{1}{3}\pi r^2 h$. Substitute $r=3$, $h=4$, $\pi=3.14$:
$$V=\frac{1}{3} \times 3.14 \times 3^2 \times 4$$
$$V=\frac{1}{3} \times 3.14 \times 9 \times 4 = 3.14 \times 3 \times 4 = 37.68$$

Step2: Compute time to drain

Time = $\frac{\text{Total Volume}}{\text{Drip Rate}}$. Substitute values:
$$t=\frac{37.68}{12}=3.14$$

Answer:

3.14 minutes