(Another) Introductory Level Calculus Question

[Wormaldson]

Homework Statement

The cross section of a canal can be modeled by a parabola.
The canal is 80 m wide at ground level and 20 m deep at its lowest point.
The canal is 0.8 km long.
Find the volume of water in the canal when it is full to ground level.

Homework Equations

Will add them once I find out what they actually are.

The Attempt at a Solution

I've deduced so far that the derivative of the parabola (if that's even relevant to the question) will cross the x-axis axis at the vertex/lowest point of the canal. This point is at 40 metres across.

Problem is, I don't know what to do with this information. I'm assuming I'm supposed to construct the equation of the parabola somehow, but I don't know how to do that.

Any help would be much appreciated.

 

[granpa]

its an integration problem

 

[Wormaldson]

its an integration problem

Thanks, that's a step in the right direction.

 

[Mark44]

Homework Statement

The cross section of a canal can be modeled by a parabola.
The canal is 80 m wide at ground level and 20 m deep at its lowest point.
The canal is 0.8 km long.
Find the volume of water in the canal when it is full to ground level.

Homework Equations

Will add them once I find out what they actually are.

The Attempt at a Solution

I've deduced so far that the derivative of the parabola (if that's even relevant to the question) will cross the x-axis axis at the vertex/lowest point of the canal. This point is at 40 metres across.

You don't need the derivative to determine this. You are given that the cross-section shape is a parabola. Any parabola can be modeled by the equation y = ax² + bx + c, for some constants a, b, and c.

Obviously, the parabola opens upward, so a > 0. You can put the vertex wherever you like, but it might be more convenient to put it at (0, -20), and the two ends at (-40, 0) and (40, 0). Use these three points to find the equation of your parabola.

Problem is, I don't know what to do with this information. I'm assuming I'm supposed to construct the equation of the parabola somehow, but I don't know how to do that.

Any help would be much appreciated.

 

[zgozvrm]

Problem is, I don't know what to do with this information. I'm assuming I'm supposed to construct the equation of the parabola somehow, but I don't know how to do that.

Sounds like you need to do some review. You should know how to do this before getting into introductory calculus.

 

[Wormaldson]

You don't need the derivative to determine this. You are given that the cross-section shape is a parabola. Any parabola can be modeled by the equation y = ax² + bx + c, for some constants a, b, and c.

Obviously, the parabola opens upward, so a > 0. You can put the vertex wherever you like, but it might be more convenient to put it at (0, -20), and the two ends at (-40, 0) and (40, 0). Use these three points to find the equation of your parabola.

Thank you sir, I think I've got it now. Will update with the working when I get the time to do it.

Sounds like you need to do some review. You should know how to do this before getting into introductory calculus.

I'm aware of that, but I don't have much of a choice, really. My exams are coming up fast, and I'm aiming to score well in them, so I have to sort of "force-feed" myself this stuff as quickly as I can.

Anyway, though, I worked out how to construct the equation for the parabola and find the integral very quickly after reading Mark's advice, so I think I'll be alright. The calculus paper in my exam is ultra-fundamental stuff, and the question I posted would be expected to be one of the most difficult questions. Hopefully that gives a better perspective of the difficulty of what I'm being tested on.