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 Short 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?

Sticky Tape

Stage: 4 Short Challenge Level: Challenge Level:1

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

Roll On

Stage: 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?

Flower Show

Stage: 3 and 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?

Running Race

Stage: 3 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?

Semicircle Stack

Stage: 4 Short Challenge Level: Challenge Level:1

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

Eyelids

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

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

Rolling Inside

Stage: 3 and 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

Stage: 3 and 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 ?

Oh So Circular

Stage: 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?

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...

Arc Area

Stage: 3 Short Challenge Level: Challenge Level:1

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

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?