Weekly Problem 36 - 2011

Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

Find the perimeter of this shape made of semicircles

Weekly Problem 13 - 2016

The circle of radius 4cm is divided into four congruent parts by arcs of radius 2cm as shown. What is the length of the perimeter of one of the parts, in cm?

Weekly Problem 37 - 2011

Rotating a pencil twice about two different points gives surprising results...

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

Weekly Problem 49 - 2006

What is the area of the shape enclosed by the line and arcs?

What is the total area enclosed by the three semicicles?

Weekly Problem 31 - 2015

The diagram shows 8 circles surrounding a region. What is the perimeter of the shaded region?

Weekly Problem 38 - 2011

Given three concentric circles, shade in the annulus formed by the smaller two. What percentage of the larger circle is now shaded?

Weekly Problem 7 - 2014

The diagram shows a shaded shape bounded by circular arcs. What is the difference in area betweeen this and the equilateral triangle shown?

Weekly Problem 18 - 2006

What is the area of the pentagon?

Weekly Problem 39 - 2011

Of these five figures, which shaded area is the greatest? The large circle in each figure has the same radius.

Weekly Problem 23 - 2014

Boris' bicycle has a bigger back wheel than front wheel. Can you work out how many revolutions the back wheel made if the front wheel did 120,000?

Weekly Problem 4 - 2012

What fraction of the volume of this can is filled with lemonade?

Weekly Problem 34 - 2010

Can you work out the fraction of the larger square that is covered by the shaded area?

Weekly Problem 52 - 2015

Four semicircles are drawn on a line to form a shape. What is the area of this shape?

Weekly Problem 5 - 2015

The diagram shows four equal discs and a square. What is the perimeter of the figure?

Weekly Problem 9 - 2016

The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

Weekly Problem 30 - 2011

Three touching circles have an interesting area between them...

Weekly Problem 26 - 2015

What are the volume and surface area of this 'Cubo Vazado' or 'Emptied Cube'?

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

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

Weekly Problem 34 - 2015

Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

Weekly Problem 11 - 2007

A circle of radius 1 rolls without slipping round the inside of a square of side length 4. Find an expression for the number of revolutions the circle makes.

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

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

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

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.

Which of these two paths made of semicircles is shorter?

Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

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

Weekly Problem 15 - 2015

In the diagram, two lines have been drawn in a square. What is the ratio of the areas marked?

Weekly Problem 13 - 2006

If three runners run at the same constant speed around the race tracks, in which order do they finish?

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?

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

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

Weekly Problem 51 - 2015

Charlie is making clown hats from a piece of cardboard. What is the maximum number he can make?

Weekly Problem 52 - 2014

Four arcs are drawn in a circle to create a shaded area. What fraction of the area of the circle is shaded?

Weekly Problem 5 - 2006

How many times does the inside disc have to roll around the inside of the ring to return to its initial position?