Question

a chemist 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 cylinder’s. the flask is filled with water, which she pours into the cylinder. to what height does the water fill the cylinder? 30 cm 15 cm 10 cm 20 cm

Explanation:

Step1: Define volume formulas

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

Step2: Set equal base/height

Let $h_{cyl}=h_{cone}=30$ cm, same radius $r$.

Step3: Equate cone volume to cylinder water volume

Let $h_w$ = water height in cylinder.
$\frac{1}{3}\pi r^2 (30) = \pi r^2 h_w$

Step4: Solve for $h_w$

Cancel $\pi r^2$: $\frac{1}{3}(30) = h_w$
$h_w = 10$

Answer:

10 cm