Perimeter, Area and Volume - Stage 4

Arclets

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".

Triangles and Petals

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?

Salinon

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?

Gutter

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?

Funnel

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 ?

Immersion

Age 14 to 16 Challenge Level:

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

Curvy Areas

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?

Track Design

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?

Fill Me up Too

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?

Semicircle Distance

Age 14 to 16 Short Challenge Level:

Can you find the shortest distance between the semicircles given the area between them?

Square in a Circle in a Square

Age 14 to 16 Short Challenge Level:

What is the ratio of the areas of the squares in the diagram?

Sinking Feeling

Age 14 to 16 Short Challenge Level:

Two vases are cylindrical in shape. Can you work out the original depth of the water in the larger vase?

Half an Annulus

Age 14 to 16 Short Challenge Level:

Can you locate the point on an annulus that splits it into two areas?

Two Paths

Age 14 to 16 Short Challenge Level:

Which of these two paths made of semicircles is shorter?

Bobbly Perimeter

Age 14 to 16 Short Challenge Level:

Find the perimeter of this shape made of semicircles

Cones and Spheres

Age 14 to 16 Short Challenge Level:

A solid metal cone is melted down and turned into spheres. How many spheres can be made?

Ratio Cut

Age 14 to 16 Short Challenge Level:

Cutting a rectangle from a corner to a point on the opposite side splits its area in the ratio 1:2. What is the ratio of a:b?

Snake Eyes

Age 14 to 16 Short Challenge Level:

Can you find the area of the yellow part of this snake's eye?

Loo Roll Emergency

Age 14 to 16 Short Challenge Level:

When the roll of toilet paper is half as wide, what percentage of the paper is left?

Candy Floss

Age 14 to 16 Short Challenge Level:

What length of candy floss can Rita spin from her cylinder of sugar?

Similar Cylinders

Age 14 to 16 Short Challenge Level:

Two similar cylinders are formed from a block of metal. What is the volume of the smaller cylinder?