big, generous, great, huge, large, thick
little, small, thin
cheese, lemon, pizza, etc.

cut
She cut a thin slice of lemon.

eat

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

slice of
a slice of bread/cake/pizza/toast

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

big, huge, large
fair, significant, sizeable, substantial (all esp. BrE)
They spend a fair slice of the budget on research and development.

narrow, small, tiny

carve, carve out
The company has managed to carve out a slice of the market for itself.

get, grab
Many investors are hoping to grab a slice of the action.

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

a slice of life
This drama provides a slice of life in 1950s Connecticut.

a slice of the action
a slice of the pie
Different groups of people will demand a bigger slice of the pie.

a slice of luck (BrE)
He needed a large slice of luck to win the game.