Thread: related rates

Coffee is poured at a uniform rate of 20 cm^3/s into a cup whose inside is shaped like a truncated cone. If the upper and lower radii of the cup are 4 cm and 2 cm and the height of the cup is 4 cm, how fast will the coffee level be rising when the coffee is halfway up? [ hint: Extend the cup downward to form a cone.]

i know that v = (1/3)(r^2)(h)
i dont know how to set r as a function of h or vice versa.

Originally Posted by larryboi7

Coffee is poured at a uniform rate of 20 cm^3/s into a cup whose inside is shaped like a truncated cone. If the upper and lower radii of the cup are 4 cm and 2 cm and the height of the cup is 4 cm, how fast will the coffee level be rising when the coffee is halfway up? [ hint: Extend the cup downward to form a cone.]

i know that v = (1/3)(r^2)(h)
i dont know how to set r as a function of h or vice versa.

following the hint ...

top radius = 4 cm

height of the extended cone = 8 cm





now work with the cone, assuming that it is filled to a height cm at ... the remaining void is the truncated cone (a frustrum).

to answer the question, note that cm from the cone's bottom when the liquid is halfway up the frustrum.