let the height of the water be h m
let the radius of the water level be r m
Make a sketch of the cross-section.
By similar triangles:
r/h = 40/10
r = 4h or h = r/4
V = (1/3)π r^2 h
= (1/3)π(4h)^2 h
= (16/3)π h^3
dV/dt = 16π h^2 dh/dt
plug in the given values and calculate
Along reservoir has the shape of a right circular cone having a radius of 40m at the top and a height of 10m at the centre. it is being filled at a constant rate of 40 m^3/min.Find the rate at which the water level is rising when the height is 5m?
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