The rate of change for the height of the ice cream is [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
The volume of an ice cream cone (V), in cubic units, is described by the following formula:
V = (1 / 3) · (π · r²) · h (1)
Where:
The rate of change for the height of the cone is derived from differentiating (1) with respect to time:
V' = (1 / 3) · (2π · r) · h · r' + (1 / 3) · (π · r²) · h'
V' = (2π / 3) · h · r' + (π / 3) · r² · h'
h' = [V' - (2π / 3) · h · r'] / [(π / 3) · r²]
Where:
If we know that V' = 10 and r' = 1 / 14, then the rate of change for the height of the cone is:
h' = [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²]
The height of the ice cream cone changes at a rate of [10 - (2π / 3) · (1 / 14) · h] / [(π / 3) · r²] units per second.
To learn more on rates of change: https://brainly.com/question/11606037
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