Other tags that relate to Cola Can
Mathematical reasoning & proof. Spheres, cylinders & cones. Interactivities. Spreadsheets. Volume and capacity. Pythagoras' theorem. Maths Supporting SET. Visualising. Surface and surface area. Cubes & cuboids.There are 179 results
Broad Topics > Thinking Mathematically > Visualising
The Spider and the Fly
Age 14 to 16
Challenge Level
A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
All Tied Up
Age 14 to 16
Challenge Level
A ribbon runs around a box so that it makes a complete loop with two parallel pieces of ribbon on the top. How long will the ribbon be?
Take Ten
Age 11 to 14
Challenge Level
Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube so that the surface area of the remaining solid is the same as the surface area of the original?
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.
Rati-o
Age 11 to 14
Challenge Level
Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?
Playground Snapshot
Age 7 to 14
Challenge Level
The image in this problem is part of a piece of equipment found in the playground of a school. How would you describe it to someone over the phone?
Framed
Age 11 to 14
Challenge Level
Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .
Tetra Square
Age 11 to 14
Challenge Level
ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.
Corridors
Age 14 to 16
Challenge Level
A 10x10x10 cube is made from 27 2x2 cubes with corridors between them. Find the shortest route from one corner to the opposite corner.
Tilting Triangles
Age 14 to 16
Challenge Level
A right-angled isosceles triangle is rotated about the centre point of a square. What can you say about the area of the part of the square covered by the triangle as it rotates?
Cutting a Cube
Age 11 to 14
Challenge Level
A half-cube is cut into two pieces by a plane through the long diagonal and at right angles to it. Can you draw a net of these pieces? Are they identical?
Convex Polygons
Age 11 to 14
Challenge Level
Show that among the interior angles of a convex polygon there cannot be more than three acute angles.
Coloured Edges
Age 11 to 14
Challenge Level
The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?
Zooming in on the Squares
Age 7 to 14
Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?
All in the Mind
Age 11 to 14
Challenge Level
Imagine you are suspending a cube from one vertex and allowing it to hang freely. What shape does the surface of the water make around the cube?
Doesn't Add Up
Age 14 to 16
Challenge Level
In this problem we are faced with an apparently easy area problem, but it has gone horribly wrong! What happened?
The Old Goats
Age 11 to 14
Challenge Level
A rectangular field has two posts with a ring on top of each post. There are two quarrelsome goats and plenty of ropes which you can tie to their collars. How can you secure them so they can't. . . .
Concrete Wheel
Age 11 to 14
Challenge Level
A huge wheel is rolling past your window. What do you see?
Linkage
Age 11 to 14
Challenge Level
Four rods, two of length a and two of length b, are linked to form a kite. The linkage is moveable so that the angles change. What is the maximum area of the kite?
One and Three
Age 14 to 16
Challenge Level
Two motorboats travelling up and down a lake at constant speeds leave opposite ends A and B at the same instant, passing each other, for the first time 600 metres from A, and on their return, 400. . . .
There and Back Again
Age 11 to 14
Challenge Level
Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
The Farmers' Field Boundary
Age 11 to 14
Challenge Level
The farmers want to redraw their field boundary but keep the area the same. Can you advise them?
Auditorium Steps
Age 7 to 14
Challenge Level
What is the shape of wrapping paper that you would need to completely wrap this model?
Baravelle
Age 7 to 16
Challenge Level
What can you see? What do you notice? What questions can you ask?
Cuboid Challenge
Age 11 to 16
Challenge Level
What's the largest volume of box you can make from a square of paper?
Packing 3D Shapes
Age 14 to 16
Challenge Level
What 3D shapes occur in nature. How efficiently can you pack these shapes together?
Eight Hidden Squares
Age 7 to 14
Challenge Level
On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?
Ten Hidden Squares
Age 7 to 14
Challenge Level
These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?
Weighty Problem
Age 11 to 14
Challenge Level
The diagram shows a very heavy kitchen cabinet. It cannot be lifted but it can be pivoted around a corner. The task is to move it, without sliding, in a series of turns about the corners so that it. . . .
Cuboids
Age 11 to 14
Challenge Level
Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?
Something in Common
Age 14 to 16
Challenge Level
A square of area 3 square units cannot be drawn on a 2D grid so that each of its vertices have integer coordinates, but can it be drawn on a 3D grid? Investigate squares that can be drawn.
Square It
Age 11 to 16
Challenge Level
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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?
Inside Out
Age 14 to 16
Challenge Level
There are 27 small cubes in a 3 x 3 x 3 cube, 54 faces being visible at any one time. Is it possible to reorganise these cubes so that by dipping the large cube into a pot of paint three times you. . . .
On the Edge
Age 11 to 14
Challenge Level
If you move the tiles around, can you make squares with different coloured edges?
Painted Cube
Age 14 to 16
Challenge Level
Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
Natural Sum
Age 14 to 16
Challenge Level
The picture illustrates the sum 1 + 2 + 3 + 4 = (4 x 5)/2. Prove the general formula for the sum of the first n natural numbers and the formula for the sum of the cubes of the first n natural. . . .
Platonic Planet
Age 14 to 16
Challenge Level
Glarsynost lives on a planet whose shape is that of a perfect regular dodecahedron. Can you describe the shortest journey she can make to ensure that she will see every part of the planet?
Around and Back
Age 14 to 16
Challenge Level
A cyclist and a runner start off simultaneously around a race track each going at a constant speed. The cyclist goes all the way around and then catches up with the runner. He then instantly turns. . . .
Picture Story
Age 14 to 16
Challenge Level
Can you see how this picture illustrates the formula for the sum of the first six cube numbers?
Cubist Cuts
Age 11 to 14
Challenge Level
A 3x3x3 cube may be reduced to unit cubes in six saw cuts. If after every cut you can rearrange the pieces before cutting straight through, can you do it in fewer?
Coke Machine
Age 14 to 16
Challenge Level
The coke machine in college takes 50 pence pieces. It also takes a certain foreign coin of traditional design...
Just Opposite
Age 14 to 16
Challenge Level
A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?
When the Angles of a Triangle Don't Add up to 180 Degrees
Age 14 to 18
This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .
Dissect
Age 11 to 14
Challenge Level
What is the minimum number of squares a 13 by 13 square can be dissected into?
NRICH is part of the family of activities in the Millennium Mathematics Project.