1. Answer Key
Q3
1. Find two non-negative numbers whose sum is 9 and so the product of the number and the
square of the other number is a maximum. (5 pts)
2. Find the circular cone of maximum volume inscribed in a sphere of radius 10-inches. (10 pts)

2. 3. Build a rectangular pen with three parallel sections using 500 ft of fencing. What dimensions will
maximize the total area of the pen? (8 pts)
4. A container in shape of a right circular cylinder with no top has a surface area of 130 ft2. What
height h and base radius r will maximize the volume of the cylinder? (8 pts)

3. 5. A sheet of cardboard 3 ft by 4 ft will be made into a box by cutting equal sized squares from
each corner and folding up the four edges. What will be the dimensions of the box with largest
volume? (5 pts)
6. Consider a rectangle of perimeter 12-inches. Form a cylinder by revolving this rectangle about
one of its edges. What dimensions of the rectangle will result in a cylinder of maximum volume?
(10 pts)