Respuesta :
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
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
The height of does water filling the cylinder is 10cm.
Given that
The chemist has an empty cylinder with a height of 30 cm and a cone-shaped flask.
The flask is the same height and has a base that is the same size as the cylinders.
Flask is filled with water which she pours into the cylinder.
We have to determine
What height does the water fill the cylinder?
According to the question
The volume of the cone is given by the following formula;
[tex]\rm V = \dfrac{1}{3}\pi r^2h[/tex]
The volume of the cylinder is given by the following formula;
[tex]\rm V = \pi r^2h[/tex]
Where r is the radius of the base and h, is the height of the cylinder.
The flask is the same height and has a base that is the same size as the cylinders.
Flask is filled with water which she pours into the cylinder.
Then,
From both equations,
The only difference in the formulas is that the formula for the cone flask is 1/3 the formula for the cylinder.
[tex]\rm V = \dfrac{1}{3}\pi r^2h= \pi r^2h\\\\ V = \dfrac{1}{3} \times 30\\\\V =10[/tex]
Hence, the height does water fill the cylinder is 10cm.
To know more about Cone click the link given below.
https://brainly.com/question/14041438
