Perimeter, Area and Volume - Stage 4

Of All the Areas

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

Blue and White

KS 3 Challenge Level:

Challenge Level:1

In the four examples below identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

Arclets

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

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:

Challenge Level:2 Challenge Level:2

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

An Unusual Shape

KS 3 Challenge Level:

Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

Salinon

KS 4 Challenge Level:

Challenge Level:1

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?

Efficient Cutting

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

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.

Gutter

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

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

Cola Can

KS 4 Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Funnel

KS 4 Challenge Level:

Challenge Level:3 Challenge Level:3 Challenge Level:3

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 ?

Immersion

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

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

Curvy Areas

KS 4 Challenge Level:

Challenge Level:1

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

Track Design

KS 4 Challenge Level:

Challenge Level:1

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

Fill Me up Too

KS 4 Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Area Stage 4 - Short Problems

KS 4 Challenge Level:

Challenge Level:1

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