Volume and capacity

problem
Cuboid-in-a-box

Age

7 to 11

Challenge level

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?
problem
More pebbles

Age

7 to 11

Challenge level

Have a go at this 3D extension to the Pebbles problem.
problem
Cylinder cutting

Age

7 to 11

Challenge level

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
problem
A jar of teddies

Age

7 to 14

Challenge level

How many teddies are in the jar? How many teddies could you fit in your classroom?
problem
The genie in the jar

Age

11 to 14

Challenge level

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?
problem
Growing rectangles

Age

11 to 14

Challenge level

What happens to the area and volume of 2D and 3D shapes when you enlarge them?
problem
Place your orders

Age

11 to 14

Challenge level

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
problem
Chocolate cake

Age

11 to 14

Challenge level

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

Age

11 to 14

Challenge level

A colourful cube is made from little red and yellow cubes. But can you work out how many of each?
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?