According to Plutarch, the Greeks found all the rectangles with
integer sides, whose areas are equal to their perimeters. Can you
find them? What rectangular boxes, with integer sides, have their
surface areas equal to their volumes?
This jar used to hold perfumed oil. It contained enough oil to fill
granid silver bottles. Each bottle held enough to fill ozvik golden
goblets and each goblet held enough to fill vaswik crystal spoons.
Each day a spoonful was used to perfume the bath of a beautiful
princess. For how many days did the whole jar last? The genie's
master replied: Five hundred and ninety five days. What three
numbers do the genie's words granid, ozvik and vaswik stand for?
Stage: 3 Challenge Level:
The width of the A4 sheet could determine the circumference of the base of the cylinder. Then the diameter of the base restricts how high the cylinder can be - can you work out the dimensions of this cylinder?
The length of the A4 sheet could determine the circumference of the base of the cylinder.
The width of the A4 sheet could determine the height of the cylinder.
The length of the A4 sheet could determine the height of the cylinder.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.