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

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

Step-by-step explanation:

Given,

Diameter of conical funnel (D) = 14 centimeters

Height of conical funnel(H) = 12 centimeters

Therefore, radius (R) = Diameter/2 = 14/2 = 7cm

We know, in conical funnel radius at height(h) = 6cm

And ratio of radius to height is always constant.

So, R/H = x/h

so, 7/12 = x/6

x = (7*6)/12

x = 3.5 cm

We have the rate of liquid flowing out at 40 cubic centimeters per second

We know, Rate = dv/dt= 40 cm3/second

dv/dt = Π\PiΠ 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

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

Hope it helps!

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