# Perimeter, Area and Volume - Stage 4

This is part of ourĀ Secondary Curriculum collection of favourite rich tasks arranged by topic.

Scroll down to see the complete collection, or explore our subcollections on Perimeter and Area in two dimensions, and Surface Area and Volume in three dimensions.

### Perimeter and Area

This selection of problems challenges students to use their understanding of perimeter and area of shapes made from circles.

### Surface Area and Volume

This selection of problems challenges students to use their understanding of surface area and volume of three dimensional shapes based on circles.

### Track Design

##### KS 4 Challenge Level:

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

### Salinon

##### KS 4 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?

### Curvy Areas

##### KS 4 Challenge Level:

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

### Arclets

##### KS 4 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".

### Triangles and Petals

##### KS 4 Challenge Level:

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

### Fill Me up Too

##### KS 4 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?

### Gutter

##### KS 4 Challenge Level:

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

### Immersion

##### KS 4 Challenge Level:

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

### Funnel

##### KS 4 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 ?

### Perimeter, Area and Volume Stage 4 - Short Problems

##### KS 4

A collection of short Stage 4 problems on area and volume.