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  All Sites - 20 items found, showing 1 to 20

  1. Arranging Six Squares - Annie Fetter
    Geometry, difficulty level 3. How many ways can you arrange six squares in the plane so that they all share an edge with at least one other square? How many of these configurations could be folded up to form a cube? ...more>>

  2. Building Boxes - Leigh Nataro
    Trig/Calc, difficulty level 2. Find the maximum volume of a rectangular prism constructed from an 8.5-inch by 11-inch piece of paper. ...more>>

  3. Chocolate, Orange, Mega-mint Swirl - Fitzgerald's Spring 2000 Class C
    Pre-Algebra, difficulty level 4. How many half-gallon cartons of ice cream can fit in the freezer? ...more>>

  4. Cubic Changes - Lisa Lavelle
    Math Fundamentals, difficulty level 4. Determine how the volume and surface area of a cube change when the edge length is changed. ...more>>

  5. Diego's Building Block - Terry Trotter
    Algebra, difficulty level 3. Find the surface area of a rectangular prism, given the volume and information about the dimensions. ...more>>

  6. Find the Volume of a Box - Annie Fetter
    Geometry, difficulty level 2. Given the surface area of three sides, find the dimensions and volume of a rectangular box. ...more>>

  7. The Great Flood - Jon Basden
    Elementary, difficulty level 3. How much "flood" water did Mr. Basden clean up with his shop vac? ...more>>

  8. Home-Made Valentine Card - Terry Trotter
    Algebra, difficulty level 2. Reuben expresses his affection for his girlfriend by making his own Valentine's Day card, described mathematically. ...more>>

  9. The Inside Lines - Larry Sue
    Discrete Math, difficulty level 4. This problem makes use of Euler's formula and some geometry to find internal diagonals of regular polyhedra: tetrahedra, octahedra, and icosahedra. ...more>>

  10. Nets of a Cube - Annie Fetter
    Geometry, difficulty level 2. When you fold up the given net of a cube, what shape is formed by the segments on the faces of the cube? ...more>>

  11. Painting a Cube - Annie Fetter
    Geometry, difficulty level 3. A large cube, made up of smaller cubes, has some of its faces painted. When it's taken apart, 24 of the small cubes have no paint on them. How big was the large cube, and how many of its faces were painted? ...more>>

  12. Pentomino Cubes - Annie Fetter
    Geometry, difficulty level 3. Given the 12 pentominoes, explain which ones can't be used as the basis for the net of a cube. Then take three of the ones that will work and explain where you can attach the sixth square to make the full net. ...more>>

  13. Picking Painted Cubes - Annie Fetter
    Geometry, difficulty level 2. A large cube, composed of smaller cubes, is painted on all sides. The edge length is five small cubes. It's then broken apart and the smaller cubes are put in a bag. What are the odds that a chosen cube is painted on three ...more>>

  14. Playing with Blocks - Annie Fetter
    Geometry, difficulty level 4. A large cube is made up of 13 double cubes like the smaller one shown, plus a single cube. What color is the single cube, and where does it have to be? ...more>>

  15. Playing with Paint - Annie Fetter
    Geometry, difficulty level 2. Explain what three-dimensional solid would make a given "trail" if it were dipped in paint and rolled on the floor. ...more>>

  16. Slicing a Cube - Annie Fetter
    Geometry, difficulty level 3. Given a cube with a surface area of 54 cm^2, find the perimeter of the square cross section and that of the largest rectangular cross section of that cube. ...more>>

  17. A Space Diagonal - Terry Trotter, MATHCOUNTS
    Algebra, difficulty level 2. Find the space diagonal of a certain cube in a sequence of cubes. ...more>>

  18. Splish Splash - Lisa Lavelle
    Math Fundamentals, difficulty level 3. Determine the ratio of my volume to T.J.'s volume. ...more>>

  19. The Square Cross Section of a Tetrahedron - Annie Fetter
    Geometry, difficulty level 3. Given a regular tetrahedron with an edgelength of 10, find the area and perimeter of the square cross section and how to get that cross section. ...more>>

  20. The Termite and the Cube - Jared Hammond
    Discrete Math, difficulty level 1. Can a termite, traveling only vertically or horizontally through a 3x3x3 Rubik-like cube, go through every cube exactly once and wind up in the very center? ...more>>


 
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