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Conical Bottle
A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?
Squirty
Using a ruler, pencil and compasses only, it is possible to construct a square inside any triangle so that all four vertices touch the sides of the triangle.
Age 14 to 16
Challenge Level
The smaller of two similar rectangles has height $2$ units; the larger rectangle has length $6$ units.
If one rectangle has twice the area of the other, find the length of the smaller rectangle.
This problem is taken from Tony Gardiner's 'Extension Mathematics Gamma' book.
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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.