Question

An irregular chunk of iron has a density of 7.87 g/cm3. A 14.5 gram chunk is added to a graduated cylinder. If the final volume of the graduated cylinder is 39.8 mL, what would be the starting volume?

Answer 1

37.96 mL

Step-by-step explanation:

From the question given above, the following data were obtained:

Density (D) of iron = 7.87 g/cm³

Mass (m) of iron = 14.5 g

Volume of Cylinder + Iron = 39.8 mL

Volume of Cylinder =?

Next, we shall determine the volume of the chunk of iron. This can be obtained as follow:

Density (D) of iron = 7.87 g/cm³

Mass (m) of iron = 14.5 g

Volume (V) of iron =?

D = m/V

7.87 = 14.5 /V

Cross multiply

7.87 × V = 14.5

Divide both side by 7.87

V = 14.5 / 7.87

V = 1.84 cm³

Recall:

1 cm³ = 1 mL

Therefore,

1.84 cm³ = 1.84 mL

Therefore, the volume of the chunk of iron is 1.84 mL.

Finally, we shall determine the starting volume of the cylinder as follow:

Volume of Cylinder + Iron = 39.8 mL

Volume of Iron = 1.84 mL.

Volume of Cylinder =?

Volume of Cylinder = (Volume of Cylinder + Iron) – Volume of Iron

Volume of Cylinder = 39.8 – 1.84

Volume of Cylinder = 37.96 mL

Therefore the starting volume of cylinder is 37.96 mL