Perimeter, Area and Volume Stage 4 - Short Problems

A collection of short Stage 4 problems on area and volume


Circle in a Semicircle

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

Weekly Problem 36 - 2011
Imagine cutting out a circle which is just contained inside a semicircle. What fraction of the semi-circle will remain?

Pencil Turning

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

Weekly Problem 37 - 2011
Rotating a pencil twice about two different points gives surprising results...

Maximised Area

Stage: 4 Short Challenge Level: Challenge Level:1

Weekly Problem 39 - 2011
Of these five figures, which shaded area is the greatest? The large circle in each figure has the same radius.

Canny Fraction

Stage: 4 Short Challenge Level: Challenge Level:1

Weekly Problem 4 - 2012
What fraction of the volume of this can is filled with lemonade?

Circle Time

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 19 - 2010
Three circles of different radii each touch the other two. What can you deduce about the arc length between these points?

Crazy Shading

Stage: 3 Short Challenge Level: Challenge Level:1

Weekly Problem 34 - 2010
Can you work out the fraction of the larger square that is covered by the shaded area?

Circled Corners

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

Weekly Problem 51 - 2010
Three circles have been drawn at the vertices of this triangle. What is the area of the inner shaded area?

Wood Pile Perimeter

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

Weekly Problem 30 - 2011
Three touching circles have an interesting area between them...

Droplets

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

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?

Penny Farthing

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

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?

Snail's Pace

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

Weekly Problem 29 - 2014
snail is at one corner of a cube. What proportion of the surface of the cube could the snail reach in one hour?

In or Out?

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

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?

Four Leaf Clover

Stage: 4 Short Challenge Level: Challenge Level:1

Weekly Problem 5 - 2015
The diagram shows four equal discs and a square. What is the perimeter of the figure?

Square Flower

Stage: 4 Short Challenge Level: Challenge Level:1

Weekly Problem 31 - 2015
The diagram shows 8 circles surrounding a region. What is the perimeter of the shaded region?

Clown Hats

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

Weekly Problem 51 - 2015
Charlie is making clown hats from a piece of cardboard. What is the maximum number he can make?

Smile

Stage: 4 Short Challenge Level: Challenge Level:2 Challenge Level:2

Weekly Problem 52 - 2015
Four semicircles are drawn on a line to form a shape. What is the area of this shape?

Semicircular Design

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

Weekly Problem 9 - 2016
The diagram to the right shows a logo made from semi-circular arcs. What fraction of the logo is shaded?

Four Parts

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

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?