Perimeter, Area and Volume Stage 4 - Short Problems


This is part of our collection of Short Problems.

You may also be interested in our longer problems on Perimeter, Area and Volume - Stage 4.

Sticky Fingers

KS 3 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 7 - 2011
Ruth wants to puts stickers on the cuboid she has made from little cubes. Will she have any stickers left over?

Droplets

KS 3 & 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?

Pencil Turning

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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

Four Parts

KS 3 & 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?

Penny Farthing

KS 3 & 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

KS 3 & 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?

Circled Corners

KS 3 & 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?

Rolling Inside

KS 3 & 4 Short Challenge Level:

Challenge Level:1

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.

Circumference and Diameter

KS 3 & 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 15 - 2008
Which of these graphs could be the graph showing the circumference of a circle in terms of its diameter ?

Semicircular Design

KS 3 & 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?

Wood Pile Perimeter

KS 3 & 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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

Flower Show

KS 3 & 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 7 - 2006
It takes four gardeners four hours to dig four circular flower beds, each of diameter 4 metres. How long will it take six gardeners to dig six circular flower beds, each of diameter six metres?

Gaudi's Design

KS 3 & 4 Short Challenge Level:

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

Weekly Problem 12 - 2015
Eight lines are drawn in a regular octagon to form a pattern. What fraction of the octagon is shaded?

Circle in a Semicircle

KS 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?

Oh So Circular

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 24 - 2008
The diagram shows two circles and four equal semi-circular arcs. The area of the inner shaded circle is 1. What is the area of the outer circle?

Semicircle Stack

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 19 - 2006
What is the total area enclosed by the three semicicles?

Maximised Area

KS 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.

Crazy Shading

KS 4 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?

Square Flower

KS 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?

Pentagonal Area

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 18 - 2006
What is the area of the pentagon?

Canny Fraction

KS 4 Short Challenge Level:

Challenge Level:1

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

Sticky Tape

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 4 - 2006
Work out the radius of a roll of adhesive tape.

Four Leaf Clover

KS 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?

Roll On

KS 4 Short Challenge Level:

Challenge Level:1

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?

Smile

KS 4 Short Challenge Level:

Challenge Level:1

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

Arc Area

KS 4 Short Challenge Level:

Challenge Level:1

Weekly Problem 49 - 2006
What is the area of the shape enclosed by the line and arcs?

Circle Time

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

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?

Emptied Cube

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 26 - 2015
What are the volume and surface area of this 'Cubo Vazado' or 'Emptied Cube'?

Trisected Triangle

KS 4 Short Challenge Level:

Challenge Level:2 Challenge Level:2

Weekly Problem 34 - 2015
Four tiles are given. For which of them can three be placed together to form an equilateral triangle?

Cut-up Square

KS 4 Short Challenge Level:

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

Weekly Problem 15 - 2015
In the diagram, two lines have been drawn in a square. What is the ratio of the areas marked?

Running Race

KS 4 Short Challenge Level:

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

Weekly Problem 13 - 2006
If three runners run at the same constant speed around the race tracks, in which order do they finish?

Eyelids

KS 4 Short Challenge Level:

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

Weekly Problem 42 - 2006
Can you work out the shaded area surrounded by these arcs?

In or Out?

KS 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?

Clown Hats

KS 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?