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coffee maker has the shape of a cone 10cm high with a radius of 6 cm at the top. The coffee maker is filled with water, and the water is allowed to drain out the bottom of the cone. Water is flowing out of the filter at a rate of 5 cubic centimerters per second. At what rate is the water level in the cone falling when it is 5cm from the bottom of the cone.

Respuesta :

nuhulawal20

Answer: the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec

Step-by-step explanation:

Given the data in the question;

H/h = R/r

10/5 = 6/r

r 1 = 30/10 = 3

Also

10/h = 6/r

r2 = 6h/10 = 3/5 × h

Volume = 1/3πr²h

V = 1/3 × π × (3/5 × h)² × h

V =  1/3 × π × 9/25 × h³

V = 3π/25 × h³

Now

dv/dt = 3π/25 × 3 × h² × dh/dt

-5 = 3π/25 × 3 × 25 × dh/dt

-5 = 3π × 3 × dh/dt

-5 = 9π × dh/dt

dh/dt = -5/9π

dh/dt = -0.1768 cm/sec

therefore, the rate of the water level in the cone falling when it is 5cm from the bottom of the cone is -0.1768 cm/sec