1. 2-D shapes Amy finds this in a book of puzzles:
[GM1.3 Core Plenary ]
Amy finds this in a book of puzzles:
A side-view of the earth is an almost perfect circle with a diameter of about km. Imagine a ribbon going once round the earth and just touching the ground. What extra length of ribbon would be needed if the ribbon was one metre above the earth?
She comes up with an answer of about 6 metres!!
Has she made a mistake?
Show all your working to support your answer.
Preamble
A rather old – but a nevertheless surprising – task.
Possible content
Using and recalling the formula for the circumference of a circle.
Resources
None.
Solution/Notes
Ribbon needed to go round once just touching = π × metres Ribbon needed to go round with 1 m gap = π × ( ) metres (some pupils may make the error of adding just 1 m forgetting they are dealing with the diameter). The extra length is therefore simply 2π which is about 6 metres – not an intuitive answer!
Original Material © Cambridge University Press 2010
Original Material © Cambridge University Press 2010