This is an extract from the book "The Elegant Universe" but I couldn't figure out why does this actually happen? How can one figure out that circumference is going to decrease or increase if a circle is drawn on different types of curved surfaces?

Why is the circumference of a circle drawn on a sphere less than the circumference of the circle of same radius drawn on a flat surface? This is an extract from the book "The Elegant Universe" but I couldn't figure out why this actually happens. How can one figure out that circumference is going to decrease or increase if a circle is drawn on different types of curved surfaces?