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kekoanabor19
15.04.2020 •
Mathematics
Suppose a right circular cone has a fixed height 3.6 inches. Use differentials to estimate the change in the volume of the cone if its height is kept constant but its radius is decreased from 1.3 inches to 1.27 inches. Answer with both an exact value and rounded to 2 decimal places. approximate change in volume: ≈ (include units in your work)
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Ответ:
dV/dt = 0,474552 in³/units of time
dV/dt = 0,47 in³/units of time
Step-by-step explanation:
Volume for the right circular cone:
V(c) = (1/3)*π*x²*h
Where x is radius of the circular base, and h the heigt
Differentiating on both sides of the equation, keeping in mind that h is constant, we get:
dV/dt = (1/3)*3,6*2*x*dx/dt (1)
Now when radius changes from 1,3 to 1,27 inches or 0,03 in in/units of time
dV/dt = (1/3)*3,6* 2*(1,3)²*dx/dt
units h in inches
radius in inches
dx/dt in inches/units of time
Then
dV/dt = 0,474552 in³/units of time
dV/dt = 0,47 in³/units of time
Ответ:
10-2=8 if you get a 10 then replace them and get a new one