The cavern ceiling is 50 feet high. The spider is 20 foot tall, so if you stood right under it, you'd need to have 30 foot reach.
Rough side view (each character is 5 feet):
SSSS------------ Ceiling (50 foot from the floor)
SSSS
SSSS
SSSS
.
.
.
.
.
X
------------- Floor
X is your position, right below the spider S. Since you measure distance from the corner of your square, even though the spider is exactly 30 feet from the ground, the edge of your square is 5 feet high, meaning if you're directly below (or one square adjacent) it, you could reach it with a spell that has 30 foot reach. If you'd want to hit it from a distance though, you'd need a spell with 60 foot reach at least (60 feet is the next increment from 30, right?).
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