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)

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

according to the triangle sum theorem, all the angles in a triangle must add up to 180 degrees. if we know one angle is already 90, we do 180-90=90. the other 2 angles must add up to 90, exactly.

step-by-step explanation:

i believe the answer is 323 ft

step-by-step explanation: