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Sagot :
The rate at which water being poured into the cup when the water level is 4 cm is [tex]192\pi[/tex] [tex]cm^3[/tex]/sec
What is rate of change?
Suppose there is a function and there are two quantities. If one quantity of a function changes, the rate at which other quantity of the function changes is called rate of change of a function.
Here,
Rate of change of volume is being calculated
Radius of conical cup (r) = 20 cm
Height of conical cup (h) = 10 cm
[tex]\frac{r}{h} = \frac{20}{10} = 2\\r = 2h[/tex]
Volume (V) of cone = [tex]\frac{1}{3}\pi r^2h\\[/tex]
[tex]\frac{1}{3}\pi (2h)^2h\\[/tex]
[tex]\frac{4}{3}\pi h^3[/tex]
[tex]\frac{dV}{dt} = \frac{d}{dt}(\frac{4}{3}\pi h^3)\\[/tex]
= [tex]4\pi h^2 \frac{dh}{dt}[/tex]
Here [tex]\frac{dh}{dt} = 3cm, h = 4cm[/tex]
[tex]\frac{dv}{dt}=4\pi \times4^2 \times 3[/tex]
[tex]192\pi[/tex] [tex]cm^3[/tex]/sec
The rate at which water being poured into the cup when the water level is 4 cm is [tex]192\pi[/tex] [tex]cm^3[/tex]/sec
To learn more about rate of change, refer to the link-
https://brainly.com/question/24313700
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