# Question:Optimization of volumes solid with constraint

## Question:Optimization of volumes solid with constraint

Maple

Hello.

I am taking an intermediate mathematics course. Now we are heading towards the finals and I have started to review all the topics we have been visiting during this semester.

Now I came across an excercise I cannot solve, taking into consideration what our lectures looks like and topics on the list my best bet is using lagrange multiplie method to optimize a multivariable function with constraints.

The task gives a shape that is drawn within the circle given by the equation: .

The shape is a hexagon with 2 vertecies on the y-axsis +- the radius 2, the other 4 vertecies are the following [+-x,+-y].

I´m told that this hexagon is spinned around the y-axis to form a solid sylinder with 2 cones. The problem is to choose both radius and hight of the cylinder in order to maximize the volume.

The first problem that I dont know how i can plot this in maple, I would like to plot both the 2d hexagon and the solid spinned around the y-axsis

Also I´m not to confident what the constraint should look like.

I know how to use the lagrange multiplier by hand and can apply that inside maple, however I would like to use this opportunity to get to know the power of maple functionality more in detail.

https://i.gyazo.com/9d9585ddb8eb719d2a5bd24a1ba1671b.png

The link provoided is an image of the hexagon, i didnt find out how to use image tags.

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