Answer:
dh/dt = 0.0566 feet / min
Explanation:
Volume per second, dV/dt = 30 cubic feet per minute
Diameter of cone = height of cone = h
at h = 15 feet, dh/dt = ?
Volume of cone is
V = πr²h
where, r be the radius of cone
According to question
radius of cone = half of diameter of cone = h /2
So,
[tex]V=\pi \times \left ( \frac{h^{2}}{4} \right )\times h[/tex]
[tex]V=\pi \times \frac{h^{3}}{4}[/tex]
Differentiate both sides with respect to h
[tex]dV/dh = \frac{\pi }{4}\times 3h^{2}\times \frac{dh}{dt}[/tex]
by substituting the values
[tex]30=\frac{3\times3.14}{4}\times 15\times 15\times \frac{dh}{dt}[/tex]
dh/dt = 0.0566 feet / min
