Resources tagged with: Volume and capacity

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Broad Topics > Measuring and calculating with units > Volume and capacity

Plutarch's Boxes

Age 11 to 14Challenge 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. . . .

Sending a Parcel

Age 11 to 14Challenge Level

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

Boxed In

Age 11 to 14Challenge Level

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

Conical Bottle

Age 14 to 16Challenge Level

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?

Three Cubes

Age 14 to 16Challenge Level

Can you work out the dimensions of the three cubes?

Tubular Stand

Age 14 to 16Challenge Level

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

Uniform Units

Age 14 to 16Challenge Level

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

Changing Areas, Changing Volumes

Age 11 to 14Challenge Level

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?

Cuboid Challenge

Age 11 to 16Challenge Level

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

Cola Can

Age 11 to 14Challenge Level

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

Funnel

Age 14 to 16Challenge Level

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 ?

Zin Obelisk

Age 11 to 14Challenge Level

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.

Colourful Cube

Age 11 to 14Challenge Level

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

In a Spin

Age 14 to 16Challenge Level

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

Concrete Calculation

Age 14 to 16Challenge Level

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. . . .

The Genie in the Jar

Age 11 to 14Challenge 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. . . .

Efficient Cutting

Age 11 to 14Challenge Level

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.

Mouhefanggai

Age 14 to 16

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.

Volume of a Pyramid and a Cone

Age 11 to 14

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.

Sliced

Age 14 to 16Challenge Level

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?

Growing Rectangles

Age 11 to 14Challenge Level

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

Thousands and Millions

Age 11 to 14Challenge Level

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

Maths Filler 2

Age 14 to 16Challenge Level

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

Maths Filler

Age 11 to 14Challenge Level

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

Chocolate Cake

Age 11 to 14Challenge Level

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

Immersion

Age 14 to 16Challenge Level

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

Fill Me Up

Age 11 to 14Challenge Level

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

Age 11 to 14Challenge Level

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

All in a Jumble

Age 11 to 14Challenge Level

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

A Jar of Teddies

Age 7 to 14Challenge Level

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