The slant height of 36 cubic a cone remains constant at 6 metres. If the radius is increasing at 5 metres per second how is the volume changing when the radius is 3 metres? What is the maximum volume?

Answer 1

r^2 + h^2 = 36
so, h=√(36-r^2)

v = π/3 r^2 √(36-r^2)
dv/dt = 3r(24-r^2)/√(36-r^2) dr/dt
So, plug in your numbers.

max volume is when r^2 = 24