At the instant when the radius of a cone is 3 inches, the volume of the cone is increasing at the rate of 9 pi cubic inches per minute. If
the height is always 3 times the radius, find the rate of change of the
radius at that instant.

The rate of change of the radius of the cone when the radius is 3 inches is 0. 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. inch/minute

yes

step-by-step explanation: