If you had 36 cubes, what different cuboids could you make?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
What size square should you cut out of each corner of a 10 x 10
grid to make the box that would hold the greatest number of cubes?
I went to the cinema with some friends last week and we decided to buy some bags of popcorn for during the movie.
My friend, Aimee, asked about the prices.
"Three for the small, five for the medium size and the large size is seven", the popcorn server replied quickly.
"Does the medium bag have twice as much in as the small size?" Aimee asked her. "Of course it does!" said the server, "The bag is double the size. See, it's taller, it's wider and it's deeper."
We estimated that the size of the small bag was 20cm by 10cm by 5cm.
I wonder if you can figure out which size belongs to which side.
We wondered what size the large bag would be. The popcorn server told us, "Why, the large size is double the size of the medium bag, of course".
"Do you mean each side is two times bigger?" asked Aimee.
"Naturally!" said the server.
Do you think she is correct?
How big would the large size bag be?
If the small bag contains one serving of popcorn, how many serving would the large bag contain?
Do you think the popcorn server was correct when she said that each bag was double the smaller size?
What do you think she should have said to better explain?
I wonder if a drum container that was 20 cm high and 10 cm across the base (the diameter) would hold more or less than the bag of popcorn.
Perhaps you could find out?
This problem is also available in French: Double Ton Popcorn, Augmente Ton Plaisir!