Answer:
dh/dt = 0.107m/min
dr/dt = 0.1435m/min
Explanation:
The volume of a cone is given by:
[tex]V = \pi*r^2*h/3[/tex]
The relationship between height and radius is:
h = 3/8 * (2*r) = 3/4 * r
Replacing this value into the volume formula:
[tex]V = \pi/4*r^3[/tex]
If we derive this equation:
[tex]dV/dt =\pi/4*3*r^2*dr/dt[/tex] Solving for dr/dt and knowing that dV/dt=15m^3/min
[tex]dr/dt = \frac{4*dV/dt}{3*\pi*r^2}=0.1435m/min[/tex]
With the relation between height and radius:
dh/dt=3/4*dr/dt = 0.107m/min
