Area Stage 4 - Short Problems

A collection of short Stage 4 problems on area and volume


Weekly Problem 39 - 2011

Stage: 4 Challenge Level: Challenge Level:1

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

Weekly Problem 4 - 2012

Stage: 4 Challenge Level: Challenge Level:1

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

Weekly Problem 3 - 2009

Stage: 3 Short Challenge Level: Challenge Level:2 Challenge Level:2

What fraction of the area of this regular hexagon is the shaded triangle?

Weekly Problem 19 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Weekly Problem 34 - 2010

Stage: 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 51 - 2010

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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

Weekly Problem 30 - 2011

Stage: 2 and 3 Short Challenge Level: Challenge Level:1

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

Weekly Problem 7 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 7 - 2014

Weekly Problem 23 - 2014

Stage: 3 and 4 Challenge Level: Challenge Level:1

Weekly Problem 23 - 2014

Weekly Problem 52 - 2014

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Weekly Problem 52 - 2014

Weekly Problem 5 - 2015

Stage: 4 Challenge Level: Challenge Level:1

Weekly Problem 5 - 2015

Weekly Problem 9 - 2016

Stage: 3 and 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

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

Weekly Problem 13 - 2016

Stage: 3 and 4 Short Challenge Level: Challenge Level:1

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?