Question

a cylinder has an empty cylinder with a height of 30 cm and a cone - shaped flask. the flask has the same height and a base that is the same size as the cylinders. the flask is filled with water, which is poured into the cylinder. to what height does the water fill the cylinder?
options:
(1) 10 cm
(2) 20 cm
(3) 15 cm
(4) the fourth options text is not fully recognized from the image

Explanation:

Step1: Define volume formulas

Volume of cylinder: $V_{cyl} = \pi r^2 h_{cyl}$
Volume of cone: $V_{cone} = \frac{1}{3}\pi r^2 h_{cone}$

Step2: Set volumes equal (same base/height)

Since $r$ and $h_{cyl}=h_{cone}=30$ cm are equal, set $V_{cyl,water}=V_{cone}$:
$\pi r^2 h = \frac{1}{3}\pi r^2 \times 30$

Step3: Solve for water height $h$

Cancel $\pi r^2$ from both sides:
$h = \frac{1}{3} \times 30$

Answer:

10 cm