Answer to Question #131371 in Calculus for Navneel Kumar

Question

A conical funnel is 14 centimeters in diameter and 12 centimeters deep. A liquid is flowing out at the rate of 40 cubic centimeters per second. How fast is the depth of the liquid falling when the level is 6 centimeters deep?

Answer 1

SOLUTION :

here given,

diameter of conical funnel (D)= 14 centimeters

so, radius (R) = D/2 = 14/2 = 7cm

height of conical funnel(H) = 12 centimeters

in canonical funnel radius at height(h) = 6cm

in canonical funnel ration of radius to height is constant.

R/H = x/h

so, 7/12 = x/6 (see in figure below)

x = (7*6)/12

x = 3.5 cm

here given that liquid is flowing out at the rate of 40 cubic centimeters per second

Rate = dv/dt= 40 cm³/second

dv/dt = $\Pi$ x² (dh/dt)

40 = 3.14 (3.5² )(dh/dt)

dh/dt = 40/(3.14*3.5*3.5)

dh/dt = 1.0399 cm/sec

ANSWER:

rate of the depth of the liquid falling = dh/dt = 1.0399 cm/sec