SOLUTION
The perimeter of the shape becomes

So from the perimeter, we now have an equation to find the height.
Now, let us find the area, A of the figure

Now, we have the equation for the area
To maximize the area, the derivative of the equation for the area must be equal to zero, so we have

So, from here, we can get r, then substitute the value to get h
Hence from the equation, r becomes

Hence the radius is 128.82 to the nearest hundredth
For the height we have

Hence the height is 128.82 to the nearest hundredth