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Broad Topics > Measures and Mensuration > Volume and capacity

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Growing Rectangles

Stage: 3 Challenge Level: Challenge Level:1

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

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Immersion

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Maths Filler

Stage: 4 Challenge Level: Challenge Level:1

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

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Cuboid Challenge

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What size square corners should be cut from a square piece of paper to make a box with the largest possible volume?

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Thousands and Millions

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Here's a chance to work with large numbers...

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All in a Jumble

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Funnel

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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 ?

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Cola Can

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Efficient Cutting

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Sending a Parcel

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Qqq..cubed

Stage: 4 Challenge Level: Challenge Level:1

It is known that the area of the largest equilateral triangular section of a cube is 140sq cm. What is the side length of the cube? The distances between the centres of two adjacent faces of. . . .

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Making Boxes

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Compare the Cups

Stage: 1 Challenge Level: Challenge Level:1

You'll need a collection of cups for this activity.

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Bottles (2)

Stage: 1 Challenge Level: Challenge Level:1

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

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Bottles (1)

Stage: 1 Challenge Level: Challenge Level:1

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

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Changing Areas, Changing Volumes

Stage: 4 Challenge Level: Challenge Level:1

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?

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Cylinder Cutting

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

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Place Your Orders

Stage: 3 Challenge Level: Challenge Level:1

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

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Chocolate Cake

Stage: 3 Challenge Level: Challenge Level:1

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

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Biology Measurement Challenge

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Analyse these beautiful biological images and attempt to rank them in size order.

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Fill Me Up

Stage: 3 Challenge Level: Challenge Level:1

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

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More Pebbles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Thirsty?

Stage: 1 Challenge Level: Challenge Level:1

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

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Next Size Up

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Uniform Units

Stage: 4 Challenge Level: Challenge Level:1

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

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Brimful 2

Stage: 5 Challenge Level: Challenge Level:1

Which of these infinitely deep vessels will eventually full up?

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Maths Filler 2

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Scientific Measurement

Stage: 4 Challenge Level: Challenge Level:1

Practice your skills of measurement and estimation using this interactive measurement tool based around fascinating images from biology.

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At the Pumps

Stage: 2 Challenge Level: Challenge Level:1

How will you find out how much a tank of petrol costs?

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Zin Obelisk

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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.

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Oh! Harry!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Cuboid-in-a-box

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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All Wrapped Up

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Tubular Stand

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Sliced

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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?

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Conical Bottle

Stage: 4 Challenge Level: Challenge Level:1

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?

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Mouhefanggai

Stage: 4

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.

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Volume of a Pyramid and a Cone

Stage: 3

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.

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The Genie in the Jar

Stage: 3 Challenge Level: Challenge Level:1

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. . . .

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More Christmas Boxes

Stage: 2 Challenge Level: Challenge Level:1

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?

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In a Spin

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Concrete Calculation

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Plutarch's Boxes

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

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. . . .

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Boxed In

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

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

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Reach for Polydron

Stage: 5 Challenge Level: Challenge Level:1

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.

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2D-3D

Stage: 5 Challenge Level: Challenge Level:1

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. . . .

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Plane to See

Stage: 5 Challenge Level: Challenge Level:1

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.

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Double Your Popcorn, Double Your Pleasure

Stage: 2 Challenge Level: Challenge Level:1

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.

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Multilink Cubes

Stage: 2 Challenge Level: Challenge Level:1

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