Maximizing+Cone+Volume

A cone is constructed from a circle by removing a sector and then connecting two radii. The volume of this cone depends on the size of the sector removed. //What is the volume of the largest cone that can be constructed from a circular piece of paper with a given diameter? What is the arc length of the removed sector?//

what the diameter is and || First, we took the derivative (Derivative) of the volume formula with respect to r. Then, we found the critical values using Wolframalpha - Critical Values From there, we plugged in r in the original equation so we had a function for volume only needing to know the diameter || volume || will give us the arc length of the removed sector || making it so none of the answers disappear off the screen too quickly ||
 * **Program** || **Explanation** ||
 * Disp "WHAT IS THE DIAMETER" || This command asks the user
 * Prompt D || prompts them to enter the number ||
 * (1/3)*pi*(D^2/6)*sqrt(((D^2)/4)-((D^2)/6))−>V || This is the equation we found to maximize the volume of the cone.
 * D/sqrt(6)−>R || This is the radius that we found using the above steps that would maximize
 * pi*D-2pi*R−>S || Subtracting the circumference of the cone from the circumference of the circle
 * 360*S/(pi*D)−>A || This finds the central angle of the removed sector ||
 * Disp "MAX VOLUME OF" || The rest of the commands displays the ||
 * Disp V || answers that were stored for each variable ||
 * Pause || This pauses the program so the user has to hit enter to continue
 * Disp "ARC LENGTH OF" || - ||
 * Disp S || - ||
 * Pause || - ||
 * Disp "CENTRAL ANGLE" || - ||
 * Disp A || - ||

(cm) || Central Angle Measure (radians) || Max Volume of Cone math (\text{cm}^3) math || Arc Length (cm) ||
 * Diameter of the Circle
 * 6 || 1.15 || 10.88 || 3.45 ||
 * 7 || 1.15 || 17.28 || 4.03 ||
 * 9 || 1.15 || 36.72 || 5.18 ||
 * 20 || 1.15 || 403.06 || 11.52 ||

As the diameter gets larger and larger, the central angle of the removed sector stays the same, but both the volume and arc length get larger.