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Ladder and Cube
A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?
Bendy Quad
Four rods are hinged at their ends to form a convex quadrilateral. Investigate the different shapes that the quadrilateral can take. Be patient this problem may be slow to load.
Age 14 to 16 Short Challenge Level:
Clare is painting the inside of a short triangular prism with a roller. The cross-section of the prism is an equilateral triangle with side length 1, and the cross-section of the roller is a circle with circumference 1. This is shown in the diagram.
What is the total length that Clare can paint?
Give an exact answer.
This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.
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NRICH is part of the family of activities in the Millennium Mathematics Project.
NRICH is part of the family of activities in the Millennium Mathematics Project.