Volume and capacity

  • Cuboid-in-a-Box
    problem

    Cuboid-In-A-Box

    Age
    7 to 11
    Challenge level
    filled star filled star filled star
    What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
  • More pebbles
    problem

    More Pebbles

    Age
    7 to 11
    Challenge level
    filled star filled star filled star
    Have a go at this 3D extension to the Pebbles problem.
  • Cylinder Cutting
    problem

    Cylinder Cutting

    Age
    7 to 11
    Challenge level
    filled star filled star filled star
    An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
  • A jar of teddies
    problem

    A Jar of Teddies

    Age
    7 to 14
    Challenge level
    filled star empty star empty star
    How many teddies are in the jar? How many teddies could you fit in your classroom?
  • The Genie in the Jar
    problem

    The Genie in the Jar

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal spoons. Each day a spoonful was used to perfume the bath of a beautiful princess. For how many days did the whole jar last? The genie's master replied: Five hundred and ninety five days. What three numbers do the genie's words granid, ozvik and vaswik stand for?

  • Two chocolate cakes with chocolate icing.
    problem

    Chocolate Cake

    Age
    11 to 14
    Challenge level
    filled star empty star empty star

    If I don't have the size of cake tin specified in my recipe, will the size I do have be OK?

  • A gold gift box with a ribbon.
    problem

    Plutarch's Boxes

    Age
    11 to 14
    Challenge level
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    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?

  • A stone obelisk on a grassy hill.
    problem

    Zin Obelisk

    Age
    11 to 14
    Challenge level
    filled star filled star empty star

    In the ancient city of Atlantis a solid rectangular object called a Zin was built in honour of the goddess Tina. Your task is to determine on which day of the week the obelisk was completed.

  • problem

    Boxed In

    Age
    11 to 14
    Challenge level
    filled star filled star filled star

    A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

  • Canny Fraction
    problem

    Canny Fraction

    Age
    14 to 16
    Challenge level
    filled star filled star empty star

    What fraction of the volume of this can is filled with lemonade?