Creating a Box: Create a box of maximum volume from a given rectangular sheet of paper.
Same but Different: Compare volume and surface area of solids.
Postal Restrictions: Find the dimensions of a cylinder-shaped package, based on USPS requirements, with the largest volume.
Changing Cubes: Explore the effect that changing the dimensions of a cube has on the surface area and volume of the cube.
Changing Cubes II: Explore the effect that changing the surface area and volume of a cube has on the dimensions of the cube.
Volume and Surface Area of a Cube: Explore what happens when you add ratios.
Designing Swimming Pools: Design a swimming pool with a particular volume.
Walking on a Box: Given a box, find the distance between opposite vertices using three different methods.
Cubes in a Box: How many cubes will fit in a box?
Integral Cubes: Can you combine the volume of two integral cubes and form another integral cube?
Submit your idea for an investigation to InterMath.