Question

A metal sample is hammered into a rectangular sheet with an area of 31.2 ft² and an average thickness of 2.30 × 10⁻⁶ cm. If the density of this sample is 7.15 g/cm³, calculate the mass of the sample in grams (g).

A) 0.0176 g
B) 0.0252 g
C) 0.0352 g
D) 0.0504 g

Answer 1

To calculate the mass of the metal sample, convert the thickness from cm to ft, find the volume of the rectangular sheet, and then multiply the density with the volume. Therefore, the correct option is B.

Step-by-step explanation:

To calculate the mass of the metal sample, we need to use the formula: mass = density × volume. First, we need to convert the thickness from cm to ft. Since there are 30.48 cm in 1 ft, the thickness is 2.30 × 10⁻⁶ cm ÷ 30.48 cm/ft = 7.546 × 10⁻⁸ ft. Next, we need to find the volume of the rectangular sheet by dividing the area by the thickness: volume = area ÷ thickness = 31.2 ft² ÷ 7.546 × 10⁻⁸ ft = 4.127 × 10⁸ ft³.

Now we can calculate the mass by multiplying the density with the volume: mass = density × volume = 7.15 g/cm³ × 4.127 × 10⁸ ft³ = 4.008 × 10⁹ g. Therefore, the mass of the sample is 4.008 × 10⁹ grams.