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

Explanation:

Step1: Recall volume formulas

The volume of a cylinder is $V_{cylinder}=\pi r^{2}h_{cylinder}$, and the volume of a cone is $V_{cone}=\frac{1}{3}\pi r^{2}h_{cone}$. Given that $h_{cylinder}=h_{cone} = 30$ cm and the bases are the same, so the radii are equal ($r$ is the same for both).

Step2: Compare volumes

Let the height of water in the cylinder be $h$. The volume of water (which is the volume of the cone) is poured into the cylinder. So $V_{cone}=V_{cylinder - filled}$. $\frac{1}{3}\pi r^{2}h_{cone}=\pi r^{2}h$. Since $r$ is non - zero, we can cancel out $\pi r^{2}$ on both sides of the equation. We get $\frac{1}{3}h_{cone}=h$.

Step3: Substitute the height of the cone

Substitute $h_{cone}=30$ cm into the equation $\frac{1}{3}h_{cone}=h$. Then $h = \frac{1}{3}\times30=10$ cm.

Answer:

10 cm