Ratio and proportion
-
-
articlePi, a very special number
Read all about the number pi and the mathematicians who have tried to find out its value as accurately as possible. -
articleRatio or proportion?
An article for teachers which discusses the differences between ratio and proportion, and invites readers to contribute their own thoughts.
-
problemPlane to see
Age16 to 18Challenge level
P is the midpoint of an edge of a cube and Q divides another edge in the ratio 1 to 4. Find the ratio of the volumes of the two pieces of the cube cut by a plane through PQ and a vertex. -
problemRule of three
Age11 to 14Challenge level
If it takes four men one day to build a wall, how long does it take 60,000 men to build a similar wall? -
problemStar gazing
Age14 to 16Challenge level
Find the ratio of the outer shaded area to the inner area for a six pointed star and an eight pointed star. -
problemRacing odds
Age11 to 14Challenge level
In a race the odds are: 2 to 1 against the rhinoceros winning and 3 to 2 against the hippopotamus winning. What are the odds against the elephant winning if the race is fair? -
problemConical bottle
Age14 to 16Challenge level
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? -
problemA shade crossed
Age14 to 16Challenge level
Find the area of the shaded region created by the two overlapping triangles in terms of a and b? -
problemArRh!
Age14 to 16Challenge level
Triangle ABC is equilateral. D, the midpoint of BC, is the centre of the semi-circle whose radius is R which touches AB and AC, as well as a smaller circle with radius r which also touches AB and AC. What is the value of r/R?