James is filling an ice cream cone. the cone is 12 cm tall and has a radius of 4 cm. if the ice cream fills the cone evenly at a rate of 1.5 cm3/s, what is the rate of change of the height when the height is 5 cm? (recall that a cone with radius r and height h as volume v = 1 3 πr2h.)

Step-by-step explanation:

Since, the volume of the cone,

Where,

r = radius,

h = height,

Differentiating equation (1) with respect to t ( time ),

Since, radius and height of cone must proportional,

i.e

From equation (1),

We have,

Hence, the rate of change of the height would be cm per sec.

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