The space shuttle ascended using two types of propulsion: (1) liquid hydrogen and oxygen stored in the external tank and burned in the main engines on the orbiter, and (2) the solid rocket boosters.
As noted in this answer, LH2/LO2 has a lot of theoretical advantages: high specific impulse (thus a higher delta v), high thrust-to-weight ratio, and low mass of the exhaust.
Suppose we redesigned the shuttle stack to remove the SRBs and expand the external tank, so all propulsion was by LH2/LO2. This would certainly save weight. However, how much volume would the new external tank occupy?
If your answer depends on increasing the number of main engines, please specify your assumptions in your answer (*1). Also, we are only replacing the propulsion for ascent; the OMS and RCS are to remain unchanged.
Bonus: I suspect such a shuttle would no longer fit in the Vehicle Assembly Building. Compare your volume to that of the VAB or another structure/building familiar to an average person. Here are a few you could use:
- Statue of Liberty: at least 622 m3
- Empire State Building: 37,000,000 ft3 = 1,000,000 m3
- Great Pyramid of Giza: 2,583,283 m3
- Vehicle Assembly Building: 129,428,000 ft3 = 3,665,000 m3
- Great Mosque of Mecca: approx. 8,000,000 m3
- Boeing Everett Factory: 13,385,378 m3
I should have been clearer with sentence (*1). The spacecraft certainly won't lift off with just the 3 SSMEs. In order to work, either there needs to be more engines, or different engines (or both). The tank would need to be redesigned, and probably the orbiter as well. I leave it up to the person answering to decide how much they want to bother changing to come up with an estimate. However, please include your assumptions in your answer.