I am supposed to use differentiation

Question

An engineering firm intends to use a cone shape to design a special container. The cone is to be made, by first cutting out a sector from a circular sheet of a pliable material, of radius 7cm, then bringing the cut edges of the remaining piece of the material together. Optimally, the firm wants to maximize the volume of the cone. As an astute Mathematician you are required to use your investigative as well as analytical skills to provide the engineering firm with the exact measurements of the optimal cone? Here are the measurements I got when I cut the circle and formed a cone and fill it with water. I cut the circle counting out 20 degrees one at a time and forming a cone every time I cut out 20 degrees. v=volume and d=degrees, 20d-102v,40d-134v,60d-149v,80d-133v,100d-129v,120d-125v,140d-113v,160d-73v,180d-66v,200d-52v,220d-39v,240d-28v,260d-17v. Just note that the volume was measured in ml. Also "20d-102v" mean that when I cut out 20 degrees from the circle and formed a cone it held 102 ml of water. If that info helps

Answer 1

To find a maximum or minimum, you find an appropriate equation (volume of a cone?) then take the derivative and then set it equal to 0 and solve.

 

 

I like the way you played around with the circle and measured the volume.  Out of those observations, it looks like you will get your maximum around the 60 degree mark.  If you get a significantly different answer, then you might want to check both methods...