Surface and surface area

  • All Tied Up
    problem

    All Tied Up

    Age
    14 to 16
    Challenge level
    A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
  • Take Ten
    problem

    Take Ten

    Age
    11 to 14
    Challenge level
    Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
  • Cubic Conundrum
    problem

    Cubic Conundrum

    Age
    7 to 16
    Challenge level
    Which of the following cubes can be made from these nets?
  • problem

    The Big Cheese

    Age
    7 to 11
    Challenge level

    Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

  • Tiles in the Garden
    problem

    Tiles in the Garden

    Age
    7 to 11
    Challenge level

    How many tiles do we need to tile these patios?

  • All Wrapped Up
    problem

    All Wrapped Up

    Age
    7 to 11
    Challenge level

    What is the largest cuboid you can wrap in an A3 sheet of paper?

  • A gold gift box with a ribbon.
    problem

    Plutarch's Boxes

    Age
    11 to 14
    Challenge level

    According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

  • Small pepper seedlings in turquoise pots.
    problem

    F'arc'tion

    Age
    14 to 16
    Challenge level

    At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.

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