Answer:
It takes 251.33 seconds to filter out full.
Step-by-step explanation:
We are given the following in the question:
Radius of cone, r = 6 cm
Depth of cone,h = 10 cm
Volume of flow rate =
[tex]\dfrac{dv}{dt} = 1.5~ cm^3/s[/tex]
Volume of cone-shaped coffee filter =
[tex]\dfrac{1}{3}\pi r^2 h[/tex]
The volume of the cone when water start drips out =
[tex]\dfrac{1}{3}\pi r^2 h - 1.5t[/tex]
Since, when the cone will be empty the volume of cone will be zero, thus we can write,
[tex]0 = \dfrac{1}{3}\pi r^2 h - 1.5t[/tex]
Putting all the values, we get,
[tex]0 = \dfrac{1}{3}\pi (6)^2 (10) - 1.5t\\\\t = \dfrac{1}{1.5}\times \dfrac{1}{3}(3.14)(6)^2(10)\\\\t = 251.33 \text{ seconds}[/tex]
Thus, it takes 251.33 seconds to filter out full.
