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# help on differentials watch

1. Water is pumped into a conical tank at a rate of 0.3m3s-1. The tank has the dimensions shown in the diagram, and the depth of the water is h metres at time t seconds. find an expression for dh/dt

the cone has diameter 4m, and height 8m overall. (sorry for lack of diagram, q is from textbook)

I keep getting 0.9/pi r^2 for my expression but apparently this is wrong...

2. (Original post by penelopecrux)
Water is pumped into a conical tank at a rate of 0.3m3s-1. The tank has the dimensions shown in the diagram, and the depth of the water is h metres at time t seconds. find an expression for dh/dt

the cone has diameter 4m, and height 8m overall. (sorry for lack of diagram, q is from textbook)

I keep getting 0.9/pi r^2 for my expression but apparently this is wrong...

Whats the equation? Where the rest of the information? No one is responding because of this.
3. (Original post by penelopecrux)
Water is pumped into a conical tank at a rate of 0.3m3s-1. The tank has the dimensions shown in the diagram, and the depth of the water is h metres at time t seconds. find an expression for dh/dt

the cone has diameter 4m, and height 8m overall. (sorry for lack of diagram, q is from textbook)

I keep getting 0.9/pi r^2 for my expression but apparently this is wrong...

The key element here is to get the relationship between the volume,V and the height, h of the water. From the cone dimensions you can see that the radius is 1/4 of the height. Now use the formula for the volume of a cone to create an equation connecting V and h. You should end up with V = (pi*h^3)/48. Now differentiate this to calculate dV/dh. Then use the chain rule and the fact that you are given dV/dt to calculate dh/dt. Hope that helps.
4. (Original post by towcestermaths)
the key element here is to get the relationship between the volume,v and the height, h of the water. From the cone dimensions you can see that the radius is 1/4 of the height. Now use the formula for the volume of a cone to create an equation connecting v and h. You should end up with v = (pi*h^3)/48. Now differentiate this to calculate dv/dh. Then use the chain rule and the fact that you are given dv/dt to calculate dh/dt. Hope that helps.
thank you!!!!!!! Finally, someone with a brain!!!!!!!

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