volume+and+surface+area+problems

1. Make a large rectangular prism out of cubes. What are the dimensions of the prism? How many cubes are in the prism?

2. Make a large cube out of cubes. What are the dimensions of the cube? How many little cubes are in the big cube?

3. Katie, a student at the world's first orbiting school, noticed that her unit cubes floated in zero gravity. If she was careful, she could even build floating geometric shapes with them.

One day Chris used the unit cubes to build a larger floating cube that was three units long on each edge. She then painted all the exposed faces of the cube red. Unfortunately, just after he finished, she sneezed, scattering the unit cubes. No cubes remained attached.

When Chris gathers the cubes, how many cubes will she find that have exactly 6 faces painted red? 5? 4? 3? 2? 1? 0 faces?

4. The entire surface of a floating rectangular prism (made from cubes) is painted blue. When the prism is taken apart, 20 cubes are found to be completely unpainted. How many total cubes were there in the prism, and what were the original dimensions?

5. //This one takes some concentrated thinking.// Some unit cubes are put together to form a larger cube. Some of the larger cube's faces are painted and then it is taken apart. 45 small cubes are found to have no paint on them. How many faces of the large cube were painted?

"I know what to do if all the faces were painted but I have no idea if only SOME of the faces were painted."--(quote from student)

6. Make every (flat) slice through a cube that goes through exactly three of the cube's corners -- no more and no less. When you are done, take the whole thing apart and count the pieces. How many are there?

7. What is the biggest cube which fits inside a sphere with a radius of 10cm?

8. What is the volume for a prism that has a surface area of 256 square centimeters?

9. The surface area of a rectangular prism is 256 square centimeters. One length is x, another is 5x, and the last is 5x-1. What is the volume?