a) 1. The problem statement, all variables and given/known data A water trough is 10m long, and a cross section has the shape of an isosceles triangle that is 1m across at the top and 50cm high. The trough is being filled with water at a rate of 0.4m^3/min. How fast is the water level rising when the water is 40cm deep? b) As a volcano erupts, pouring lava over its slope, it maintains the shape of a cone, with height twice as large as the radius of the base. If the height is increasing at a rate of 0.5 m/s, and all the lava stays on the slopes, at what rate is the lava pouring out of the volcano when the volcano is 50m high? 2. Relevant equations h=height w=width 3. The attempt at a solution a) dV/dt = 0.4m^3/min V=(1/2)hw(10) =5hw w/1=h/0.5 w=2h V=5hw = 5h(2h) = 10h^2 dV/dt=20hh' 0.4 = 20(0.4)h' 0.05=h' I am almost sure it is correct but I am just looking for a confirmation. I will add units of course later. b) h' = 0.5m r=(h/2) h=50 v'=? I think we are searching for the rate the volume decreases..so it would be 981.25m^3/s.