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Nurturing young mathematicians: teacher webinars

30 April (Primary), 1 May (Secondary)

30 April (Primary), 1 May (Secondary)

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There are **54** NRICH Mathematical resources connected to **Volume and capacity**, you may find related items under Measuring and calculating with units.

Problem
Primary curriculum
Secondary curriculum
### Pouring Problem

What do you think is going to happen in this video clip? Are you surprised?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Colourful Cube

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bottles (2)

In this activity focusing on capacity, you will need a collection of different jars and bottles.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Bottles (1)

For this activity which explores capacity, you will need to collect some bottles and jars.

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Changing Areas, Changing Volumes

How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Place Your Orders

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fill Me up Too

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Discuss and Choose

This activity challenges you to decide on the 'best' number to use in each statement. You may need to do some estimating, some calculating and some research.

Age 5 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Fill Me Up

Can you sketch graphs to show how the height of water changes in different containers as they are filled?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Thirsty?

Can you lay out the pictures of the drinks in the way described by the clue cards?

Age 5 to 7

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Next Size Up

The challenge for you is to make a string of six (or more!) graded cubes.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Growing Rectangles

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Immersion

Various solids are lowered into a beaker of water. How does the water level rise in each case?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maths Filler

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cuboid Challenge

What's the largest volume of box you can make from a square of paper?

Age 11 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### All in a Jumble

My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Oh! Harry!

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Funnel

A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cola Can

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Efficient Cutting

Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sending a Parcel

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Cuboids

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Making Boxes

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Uniform Units

Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Brimful 2

Which of these infinitely deep vessels will eventually full up?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Maths Filler 2

Can you draw the height-time chart as this complicated vessel fills with water?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Zin Obelisk

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.

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Cuboid-in-a-box

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### All Wrapped Up

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

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Tubular Stand

If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Sliced

An irregular tetrahedron has two opposite sides the same length a and the line joining their midpoints is perpendicular to these two edges and is of length b. What is the volume of the tetrahedron?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Conical Bottle

A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?

Age 14 to 16

Challenge Level

Article
Primary curriculum
Secondary curriculum
### Mouhefanggai

Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.

Age 14 to 16

Article
Primary curriculum
Secondary curriculum
### Volume of a Pyramid and a Cone

These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.

Age 11 to 14

Problem
Primary curriculum
Secondary curriculum
### The Genie in the Jar

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### More Christmas Boxes

What size square should you cut out of each corner of a 10 x 10 grid to make the box that would hold the greatest number of cubes?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### In a Spin

What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Concrete Calculation

The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?

Age 14 to 16

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plutarch's Boxes

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?

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Boxed In

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

Age 11 to 14

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Reach for Polydron

A tetrahedron has two identical equilateral triangles faces, of side length 1 unit. The other two faces are right angled isosceles triangles. Find the exact volume of the tetrahedron.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### 2D-3D

Two circles of equal size intersect and the centre of each circle is on the circumference of the other. What is the area of the intersection? Now imagine that the diagram represents two spheres of equal volume with the centre of each sphere on the surface of the other. What is the volume of intersection?

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Plane to See

P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex.

Age 16 to 18

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Double Your Popcorn, Double Your Pleasure

We went to the cinema and decided to buy some bags of popcorn so we asked about the prices. Investigate how much popcorn each bag holds so find out which we might have bought.

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### The Big Cheese

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?

Age 7 to 11

Challenge Level

Problem
Primary curriculum
Secondary curriculum
### Multilink Cubes

If you had 36 cubes, what different cuboids could you make?

Age 7 to 11

Challenge Level