G12 College Algebra
Project R – Area, Volume and Optimization
1. Find surface area and volume of the irregular shape
2. Craft an origami elephant
3. Estimate the surface area of the elephant and describe your methodology in finding this
estimate
4. Estimate the volume of the elephant describe your methodology in finding this estimate
5. Optimization Problem 1: Maximize Volume
If 1200 cm2 of material is available to make a box with a square base and an open top, find the
largest possible volume of the box.
6. Optimization Problem 2: Max Cone Problem
 Consider a circle radius 10cm
 A sector x° is cut from the circle
 The resulting shape is folded in to the curved surface area of the cone
 What value of ‘x’ will generate the cone with the largest volume?
7. Optimization Problem 3: Minimize Surface Area
A cylindrical can is to be made to hold 10 L of oil. Find the dimensions that will minimize the
cost of the metal to manufacture the can
If you go to your cupboard or your supermarket with a ruler, you will discover that the height is
usually greater than the diameter. The material for the cans is cut from sheets of metal. The
cylindrical sides are formed by bending rectangles; these rectangles are cut from the sheet
with little or no waste. But if the top and bottom discs are cut from squares of side (as in the
figure), this leaves considerable waste metal, which may be recycled but has little or no value
to the can makers. A more efficient packing of the discs is obtained by dividing the metal sheet
into hexagons and cutting the circular lids and bases from the hexagons
8. Do research on Honeycomb Theorem (Hayes) and describe the details.
9. State Plateau’s problem and do research on Mathematics of Soap Bubble.