Ask HN: Maths problem – shape and size for fondant covering a round cake

I'm making my son's birthday cake - a round sponge, about 20cm tall and 30cm in diameter. I need to lay fondant icing over the top. The recipe suggested cutting into a rough square of 40cm, laying it on top, cutting away the leftovers.

In the midst of this, I tried to work out what size and shape of fondant icing I would need to perfectly cover the cake with one piece of icing and no leftovers.

Would it be a perfect circle with a diameter of 50cm (i.e. 30cm diameter + 20cm height)?