Age 14 to 16
Challenge Level
Perimeter and Area
This selection of problems challenges you to use your understanding of perimeter and area of shapes made from circles.
Age 14 to 16
Challenge Level
Surface Area and Volume
This selection of problems challenges you to use your understanding of surface area and volume of three dimensional shapes based on circles.
F'arc'tion
Age 14 to 16 Short
Challenge Level
At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and paper.
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?
Perimeter, Area and Volume Short Problems
Age 11 to 16
A collection of short problems on area and volume.
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?
Ratio of Areas
Age 14 to 16 Short
Challenge Level
What is the ratio of the area of the hexagon to the area of the triangle?
NRICH is part of the family of activities in the Millennium Mathematics Project.