Other tags that relate to Four or Five
Area - circles, sectors and segments. Volume and capacity. Area - squares and rectangles. Perimeter. 2D shapes and their properties. Quadrilaterals. Ratio. Area - triangles, quadrilaterals, compound shapes. Curious. Pythagoras' theorem.There are 30 results
Broad Topics > Measuring and calculating with units > Volume and capacity
Growing Rectangles
Age 11 to 14 Challenge Level:
What happens to the area and volume of 2D and 3D shapes when you enlarge them?
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?
Boxed In
Age 11 to 14 Challenge Level:
A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?
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?
Tubular Stand
Age 14 to 16 Challenge Level:
If the radius of the tubing used to make this stand is r cm, what is the volume of tubing used?
Changing Areas, Changing Volumes
Age 11 to 14 Challenge 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?
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?
Maths Filler
Age 11 to 14 Challenge Level:
Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?
Maths Filler 2
Age 14 to 16 Challenge Level:
Can you draw the height-time chart as this complicated vessel fills with water?
Cuboid Challenge
Age 11 to 16 Challenge Level:
What's the largest volume of box you can make from a square of paper?
Cola Can
Age 11 to 14 Challenge 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 16 Challenge 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 ?
Efficient Cutting
Age 11 to 14 Challenge 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.
Sending a Parcel
Age 11 to 14 Challenge Level:
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
Sliced
Age 14 to 16 Challenge 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?
In a Spin
Age 14 to 16 Challenge Level:
What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
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. . . .
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.
All in a Jumble
Age 11 to 14 Challenge Level:
My measurements have got all jumbled up! Swap them around and see if you can find a combination where every measurement is valid.
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. . . .
Conical Bottle
Age 14 to 16 Challenge 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?
Immersion
Age 14 to 16 Challenge Level:
Various solids are lowered into a beaker of water. How does the water level rise in each case?
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.
Fill Me Up
Age 11 to 14 Challenge Level:
Can you sketch graphs to show how the height of water changes in different containers as they are filled?
Concrete Calculation
Age 14 to 16 Challenge 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. . . .
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?
Uniform Units
Age 14 to 16 Challenge Level:
Can you choose your units so that a cube has the same numerical value for it volume, surface area and total edge length?
Zin Obelisk
Age 11 to 14 Challenge 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.
NRICH is part of the family of activities in the Millennium Mathematics Project.