Perimeter, Area and Volume - Stage 4

Arclets

KS 4 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?

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?

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?

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?

Semicircle Distance

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Square in a Circle in a Square

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Sinking Feeling

KS 4 Short Challenge Level:

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

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

Half an Annulus

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Bobbly Perimeter

KS 4 Short Challenge Level:

Challenge Level:1

Find the perimeter of this shape made of semicircles

Cones and Spheres

KS 4 Short Challenge Level:

Challenge Level:1

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

Ratio Cut

KS 4 Short Challenge Level:

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

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

KS 4 Short Challenge Level:

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

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

Loo Roll Emergency

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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