**"Surface area"**

## Blocks, Bricks and Boxes

*By toni On 5 February, 2021 · Leave a Comment*

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units.

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 […]

## Enlargement

*By toni On 11 October, 2020 · Leave a Comment*

Make enlargements of the coloured shapes by fitting together four identical smaller shapes.

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 […]

## Tops

*By toni On 19 July, 2020 · Leave a Comment*

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 […]

## Years 9 – 12 Surprise Ratios

*By toni On 3 May, 2020 · Leave a Comment*

A circle of radius r and centre O, is inscribed in a triangle with edges of lengths a, b and c.

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 […]

## Which has the smallest surface area?

*By Elizabeth Turok On 21 March, 2020 · Leave a Comment*

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 […]

## Squareflake Fractal

*By toni On 14 September, 2019 · Leave a Comment*

1. If the red square has area 1 square unit. What is the area enclosed by the stage 1 squareflake?

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 […]

## Same Volume

*By toni On 29 October, 2017 · Leave a Comment*

What is the volume of this cuboid?

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?

Click here for Notes for Teachers.

[…]

## Woodwork

*By toni On 29 July, 2017 · Leave a Comment*

This stand is made from cylindrical wooden dowel of diameter 1 cm joined at the corners with 45 degree mitres.

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 […]

## Painted Cube

*By toni On 5 November, 2016 · 22 Comments*

Imagine a large cube made up from 27 small red cubes each measuring 1 cm by 1 cm by 1 cm. What is its volume?

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 […]

## Cola Can

*By toni On 18 February, 2016 · Leave a Comment*

An aluminium can contains 330 ml of cola.

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 […]

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