Is there more than one?
It is quite easy to find a few solutions. The big challenge is to find all possible solutions.
Can you provide a convincing argument that you have found […]
How much longer are the edges (the linear scale factor of the enlargement)?
How much bigger is the area (the area scale factor of the enlargement)?
Now look at the illustration of the 3-dimensional solids. One is […]
For your company, you have to design spinning tops made from two pieces glued together, a hemisphere and a cone, and you have to plan how they will be manufactured, packaged and sold.
(1) The radius of the circular surface where the pieces are glued together is 3 cm. The slant […]
Find the area and circumference of the circle.
Find the area and the perimeter of the triangle.
What do you notice about the ratios of the two areas and the ratios […]
This picture shows a rectangular prism made from 36 cubes.
How many different rectangular prisms can you make from 36 cubes?
Do they all have the same volume? Why or why not?
Do they all have the same surface area? Why or why not?
Take the area of each face of […]
2. What is the area enclosed by the stage 2 squareflake? What about the stages 3 and 4 squareflakes?
3. If replacing each line segment on the edge with the zig-zag is […]
How many other cuboids with whole number dimensions have the same volume?
Do any of them have the same surface area?
Which has the biggest surface area? Which has the smallest?
How many have a square cross section?
The external dimensions of the stand are 10 cm by 10 cm.
What are the volume and surface area of the stand?
The sketch below shows how I marked […]
Imagine dipping the large cube into a pot of yellow paint so the whole outer surface is covered. What is its surface area?
Now imagine breaking the […]
If the can’s diameter is 6 cm what is the can’s height?
Suppose the can’s height is 10 cm, what does the diameter have to be?
Which of these two cans uses the least aluminium?
If you could choose any diameter which dimensions for the can […]