For a cone, radius and height always satisfy h = 2r. If r increases at 1 cm s⁻¹, find dV/dt at r = 3 cm.
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Question

For a cone, radius and height always satisfy h = 2r. If r increases at 1 cm s⁻¹, find dV/dt at r = 3 cm.

G1 Physics · Accepted Answer

Since h=2r: V=πr²(2r)/3 = 2πr³/3. dV/dt=2πr² dr/dt. At r=3 and dr/dt=1: dV/dt=18π cm³ s⁻¹.