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### Number and algebra

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### Advanced mathematics

# Perimeter, Area and Volume - Stage 4

### Track Design

### Salinon

### Curvy Areas

### Arclets

### Triangles and Petals

### Fill Me up Too

### Gutter

### Immersion

### Funnel

### Perimeter, Area and Volume Short Problems

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Age 14 to 16

Challenge Level

Where should runners start the 200m race so that they have all run the same distance by the finish?

Age 14 to 16

Challenge Level

This shape comprises four semi-circles. What is the relationship between the area of the shaded region and the area of the circle on AB as diameter?

Age 14 to 16

Challenge Level

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

Age 14 to 16

Challenge Level

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

Age 14 to 16

Challenge Level

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

Age 14 to 16

Challenge Level

In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?

Age 14 to 16

Challenge Level

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

Age 14 to 16

Challenge Level

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

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 ?

Age 11 to 16

A collection of short problems on area and volume.