Question

Given the density of Au is 19.3 g/cm3, determine the mass of gold (in grams) in an ingot with the dimensions of 10.0 in × 4.00 in × 3.00 in.

1) 3.80 × 10⁴
2) 102
3) 2.32 × 10³
4) 0.161
5) none of the above

Answer 1

To determine the mass of gold in the ingot, first convert the ingot's dimensions to centimeters, calculate the volume, then multiply by the density of gold. The mass is approximately 3.80 × 10⁴ grams.

Step-by-step explanation:

To determine the mass of gold in an ingot with the dimensions of 10.0 in × 4.00 in × 3.00 in, we need to first convert these dimensions into centimeters as the density of gold is given in g/cm³.

Using the conversion of 1 inch = 2.54 cm, the dimensions in centimeters will be: 10.0 in × 2.54 cm/in = 25.4 cm, 4.00 in × 2.54 cm/in = 10.16 cm, and 3.00 in × 2.54 cm/in = 7.62 cm. Now, we can calculate the volume of the ingot in cubic centimeters: V = 25.4 cm × 10.16 cm × 7.62 cm = 1963.13888 cm³.

Then, using the density of gold (d = 19.3 g/cm³), we can Remove Unwanted Space of gold: mass = density × volume = 19.3 g/cm³ × 1963.13888 cm³ = 37917.7816 grams.

So, the mass of the ingot in grams is approximately 3.80 × 10⁴ grams. Therefore, the correct answer is: 1) 3.80 × 10⁴.