Question

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)

Answer 1

dV/dt = 0,474552 in³/units of time

dV/dt = 0,47 in³/units of time

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