# Resources tagged with: Circumference and arc length

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Measuring and calculating with units > Circumference and arc length

##### Age 16 to 18 Challenge Level:

A belt of thin wire, length L, binds together two cylindrical
welding rods, whose radii are R and r, by passing all the way
around them both. Find L in terms of R and r.

##### Age 16 to 18 Challenge Level:

Two places are diametrically opposite each other on the same line of latitude. Compare the distances between them travelling along the line of latitude and travelling over the nearest pole.

##### Age 16 to 18 Challenge Level:

Use simple trigonometry to calculate the distance along the flight
path from London to Sydney.

##### Age 14 to 16 Challenge Level:

Find the perimeter and area of a holly leaf that will not lie flat
(it has negative curvature with 'circles' having circumference
greater than 2πr).

##### Age 14 to 16 Challenge Level:

An equilateral triangle rotates around regular polygons and
produces an outline like a flower. What are the perimeters of the
different flowers?

##### Age 14 to 16 Challenge Level:

The ten arcs forming the edges of the "holly leaf" are all arcs of
circles of radius 1 cm. Find the length of the perimeter of the
holly leaf and the area of its surface.

##### Age 14 to 16 Challenge Level:

Where should runners start the 200m race so that they have all run the same distance by the finish?

##### Age 16 to 18

Imagine a rectangular tray lying flat on a table. Suppose that a plate lies on the tray and rolls around, in contact with the sides as it rolls. What can we say about the motion?

##### Age 14 to 18 Challenge Level:

By inscribing a circle in a square and then a square in a circle
find an approximation to pi. By using a hexagon, can you improve on
the approximation?

##### Age 14 to 16 Challenge Level:

Each of the following shapes is made from arcs of a circle of radius r. What is the perimeter of a shape with 3, 4, 5 and n "nodes".

##### Age 14 to 16 Challenge Level:

P is a point on the circumference of a circle radius r which rolls,
without slipping, inside a circle of radius 2r. What is the locus
of P?

##### Age 14 to 16 Challenge Level:

A circular plate rolls in contact with the sides of a rectangular
tray. How much of its circumference comes into contact with the
sides of the tray when it rolls around one circuit?

##### Age 16 to 18 Challenge Level:

Find the distance of the shortest air route at an altitude of 6000
metres between London and Cape Town given the latitudes and
longitudes. A simple application of scalar products of vectors.

##### Age 16 to 18 Challenge Level:

A circular plate rolls inside a rectangular tray making five
circuits and rotating about its centre seven times. Find the
dimensions of the tray.

##### Age 11 to 16 Challenge Level:

A security camera, taking pictures each half a second, films a
cyclist going by. In the film, the cyclist appears to go forward
while the wheels appear to go backwards. Why?