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? 20 cm 15 cm 10 cm 30 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 $V_{cone}=\frac{1}{3}\pi r^{2}h_{cone}$.

Step2: Compare volumes

Since the base - radius ($r$) and height ($h$) of the cone and the cylinder are the same. Let $h = h_{cylinder}=h_{cone}=30$ cm. The volume of the cone is one - third of the volume of the cylinder with the same base and height.

Step3: Calculate height in cylinder

When the water from the full - cone is poured into the cylinder, the volume of water is $V = V_{cone}=\frac{1}{3}\pi r^{2}h$. Let the height of water in the cylinder be $h_{1}$. Then $V=\pi r^{2}h_{1}$. Since $V = V_{cone}=\frac{1}{3}\pi r^{2}h$, we have $\pi r^{2}h_{1}=\frac{1}{3}\pi r^{2}h$. Canceling out $\pi r^{2}$ on both sides, we get $h_{1}=\frac{1}{3}h$. Substituting $h = 30$ cm, we find $h_{1}=10$ cm.

Answer:

10 cm