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Gym Bag

Age 11 to 16
Challenge Level
The drawstring bag is made from 2 shapes: a circle and a rectangle, which together make a cylinder.

The circle must be big enough to contain the trainers, which have a circumference of nearly 60cm.
Circumference of a circle=  x diameter
So the diameter = 60 /Ï€
We now have to add an extra 1cm either side for the seams. So the new diameter = (60 / π) + 2

As for the rectangle, it must fit around the circle as a cylinder, and be as long as the trainers, so it must measure 60cmx30cm. We then need to leave 1cm each side for the seam, plus an extra 2cm on the opposite side to the one that will be attached to the circle, for the drawstring (a total of 3 extra cm).

For simplicity's sake, we can say that this takes up the same room as a rectangle measuring 62cm x 34cm.

Jo has a piece of fabric measuring 100cm x 50cm. We need to see if the rectangle and the circle will fit on this piece of fabric. First the rectangle:

We can see from the space left that the circle will fit on the piece of fabric if the diameter of the circle is less than 38cm.
The diameter of the circle = (60/Ï€) + 2 = 21.1
So both shapes will fit on the fabric, and her gym bag will fit her trainers!