This was a tricky problem, but many of you tackled it successfully. Your solutions depended on whether you assumed that you could cut the paper or not. Rachel from Charter Primary said:

I solved this problem by drawing a net.

The length of my cuboid was $38 \; \text{cm}$. The width of my cuboid was 14cm. The depth of my cuboid was $1\; \text{cm}$.

I tried to make the unused space as small as possible.

So, Rachel's solution kept the paper in one piece (as you would usually do when you wrap a present, for example).

This gives a cuboid with the maximum possible surface area ($1168 \;\text{cm}^2$).

I wonder how you arrived at this solution, Rachel? How many differently-sized cuboids did you try before you discovered this was the largest? Rohaan from Longbay Primary looked at it in a different way, assuming that you could cut the paper:

We decided to find a cuboid that that had a surface area that matched with the wrapping paper (

1200 {cm}^{2}

We made a starting estimate of a cuboid that was $1 \times 20 \times 20$ . It had a surface area of $880 {cm}^{2}$ .

Then we thought there could be a bigger cuboid that would fit. We wondered by how much the cuboid's surface area would go up if we changed its measurements from $1 \times 20 \times 20$ to $2 \times 20 \times 20$ . It went up $80 {cm}^{2}$ .

We thought if we changed it to $3 \times 20 \times 20$ it would go up by $80 {cm}^{2}$ again. It did. We went up until we reached $5 \times 20 \times 20$ which had a surface area of exactly $1200 {cm}^{2}$ . It matched the surface area of the wrapping paper.

Just to make sure it fitted, we drew up the surface area ( $1200 {cm}^{2}$ ) on a piece of A3 paper. It fitted!

Did anyone try to find the cuboid with the largest volume that could be wrapped up in this paper? That's another challenge for you!