An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing out of the vertex of the container at a rate of 35 /sec , how fast is the depth of the water dropping when the height is 5in?
An inverted cone has a diameter of 42 in and a height of 15in. If the water flowing out of the vertex of the container at a rate of 35 /sec , how fast is the depth of the water dropping when the height is 5in?
Volume of the cone V = 1/3*π*r^2*h.....(1)
You want to find dh/dt. So you have to find r in terms of h.
r and h are proportional tp R and H, where R = 21" and H = 15".
So R/H = r/h.
So r = (R/H)*h.
Substitute this value in the eq.(1) and find dV/dt.
dV/dt is given. Find dh/dt.