Question

A conical funnel has radius __4 cm__ and height __8 cm__. Coffee is draining from the funnel at a constant rate of [{MathJax fullWidth='false' \frac{1.3 cm^3}{sec}. }] (a) What is the depth of the coffee when there are [{MathJax fullWidth='false' 100 cm^3 }]of coffee remaining in the funnel? Do you need calculus for this part? (b) How fast is the level dropping when there are [{MathJax fullWidth='false' 100 cm^3 }] of coffee in the funnel? Do you need calculus for this part? (c) How long does it take for the funnel to drain? Do you need calculus for this part of the problem?

Answer 1

Answer:

solved

Step-by-step explanation:

v = πr²h/3 = 4²πx8 = 134 cm³ , r/h = 4/8 = 1/2 , r = h/2

v = πh³/12

dv/dt = πh²dh/dt ÷4

4dv/dt = πh²dh/dt

a ) 100 = πh³/12 , h³ = 1200/π , h = 7.25cm.

No need for calculus

b) 1.3 x4 = 7.25²πdh/dt , dh/dt = 5.2/52.5625π = 0.0315 cm/sec

yes

c) time to drain the funnel = 134cm³ ÷ 1.3cm³/sec = 103.08 sec

No need for calculus