The dimensions of a conical funnel are shown below: A conical funnel is shown with the height of the cone as 4 inches and the radius of the base as 3 inches. 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.) 2.35 minutes 4.71 minutes 1.57 minutes 3.14 minutes

Accepted Solution

[tex]\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}\quad \begin{cases} r=radius\\ h=height\\ -----\\ r=3\\ h=4 \end{cases}\implies V=\cfrac{\pi 3^2\cdot 4}{3}\implies V=12\pi [/tex]

now, when she closed the funnel and filled it up, that's how much liquid it took in.  Then it's dripping 12 in³ every minute, how long will it take to lose all the volume?

[tex]\bf \begin{array}{ccll} in^3&minute\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 12&1\\ 12\pi &m \end{array}\implies \cfrac{12}{12\pi }=\cfrac{1}{m}\implies m=\cfrac{12\pi \cdot 1}{12}[/tex]