Chemist has an empty cylinder with a height of 30 cm and a cone shaped flask. the flask is the same height and a base that is the same size as the cylinders. flask is filled with water which she pours into the cylinder. what height does the water fill the cylinder

It fills the cylinder up to 10 cm.

The volume of a cylinder is given by the formula
V = πr²h, where r is the radius of the base and h is the height of the cylinder.

The volume of a cone is given by the formula 
V = 1/3πr²h, where r is the radius of the base and h is the height of the cylinder.

Since the base of the flask and the cylinder are the same, this means r is the same number in both formulas.
Since the height of the flask and the cylinder are the same, this means h is the same number in both formulas.

This means that the only difference in the formulas is that the formula for the cone flask is 1/3 the formula for the cylinder.

The water that fills the cone flask will fill 1/3 of the cylinder; 1/3(30) = 10