Answer:
The rate of change of the radius of the cone when the radius is 3 inches is 0.[tex]\overline 3[/tex] inch/minute
Step-by-step explanation:
The given parameters are;
The radius of the cone = 3 inches
dV/dt = 9·π in.³/min
The height, h = 3 × Radius, r
The formula for the volume of a cone, V is V = 1/3×π×r²×h = 1/3×π×r²×3×r = π·r³
Therefore, we have;
dV/dt = dV/dr × dr/dt
dV/dr =3·π·r²
∴ dr/dt = dV/dt/(dV/dr) = 9·π/(3·π·r²) = 3/r²
When r = 3 inches, we have;
dr/dt = 3/r² = 3/(3²) = 1/3 inch/minute
The rate of change of the radius of the cone when the radius is 3 inches = 0.[tex]\overline 3[/tex] inch/minute
