Could We Build a Dyson Sphere Around the Sun Using Jupiter for Raw Materials?

Long-time Slashdot reader schwit1 shared this report from Futurism:
We'd need an astronomical amount of resources to construct a Dyson sphere, a giant theoretical shell that would harvest all of a given star's energy, around the Sun. In fact, as science journalist Jaime Green explores in her new book "The Possibility of Life," we'd have to go as far as to demolish a Jupiter-sized planet to build such a megastructure, a concept first devised by physicist Freeman Dyson in 1960...
Not everybody agr