big, generous, great, huge, large, thick | considerable, fair, significant, sizeable, substantial
They spend a fair slice of the budget on research and development.

small, thin | cheese, lemon, pizza, etc.

cut
She cut a thin slice of lemon.

in ~s
The sausage is also sold pre-packed in slices.

~ of
a slice of toast The agency takes a large slice of the profits.

cut sth into slices
He cut the meat into thick slices.

finely, thinly
Slice the bread thinly.

thickly | neatly | off, up
Slice up the mushrooms and fry them.

into
The axe sliced into her shoulder.

off
slicing pieces off the joint of meat

through
The knife sliced through his ear.

slice sth in half/two
Slice the onion in two.