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 20 cm 30 cm 15 cm

Explanation:

Step1: Recall volume formulas

Volume of a cylinder \( V_{cylinder}=\pi r^{2}h_{cylinder} \). Volume of a cone \( V_{cone}=\frac{1}{3}\pi r^{2}h_{cone} \).

Step2: Set up the relationship

Since \( r_{cylinder} = r_{cone}\) (same - sized base) and \( h_{cylinder}=h_{cone} = 30\) cm. Let the height of water in the cylinder be \( h\). The volume of water (volume of the cone) is equal to the volume of water in the cylinder. So \( V_{cone}=V_{cylinder - water}\). Substituting the formulas: \(\frac{1}{3}\pi r^{2}\times30=\pi r^{2}h\).

Step3: Solve for \( h\)

Cancel out \(\pi r^{2}\) from both sides of the equation \(\frac{1}{3}\times30 = h\).

Answer:

\(10\) cm