Question

A 100 ml graduated cylinder with an inside diameter of 3.2 cm contains 34.0 g of gasoline and 34.0 g of water. what is the combined height of the two liquid layers

Answer 1

The volume of cylinder is 100 mL, inner diameter is 3.2 cm thus, radius will be:

$r=\frac{d}{2}=\frac{3.2 cm}{2}=1.6 cm$

Volume of layer formed=$\pi r^{2}h$...... (1)

Volume of layer is also equal to sum of volume of gasoline and water.

Density of gasoline is $0.702 g/cm^{3}$ and mass is 34 g thus, volume of gasoline will be:

$V=\frac{m}{d}=\frac{34 g}{0.702 g/cm^{3}}=48.43 cm^{3}$

Now, density of water is $1 g/cm^{3}$ and mass is 34 g thus, volume of water will be:

$V=\frac{m}{d}=\frac{34 g}{1 g/cm^{3}}=34 cm^{3}$

Adding both the volumes, volume of layer will be:

$Volume of layer=48.43 cm^{3}+34 cm^{3}=82.43cm^{3}$

Putting the values in equation (1) to solve for height of the layer,

$h=\frac{volume of layer}{\pi r^{2}}=\frac{82.43 cm^{3}}{3.14\times 1.6 cm\times 1.6 cm}=10.25 cm$

Thus, height of layer is 10.25 cm