Answer:
40.0 kg
Explanation:
The dimensions of the ingot tell us how much volume it has. Then we multiply that volume by the density of gold to found the mass.
The trouble here is that the dimensions are in inches, but the density term is in cubic centimeters. So we'll need to convert units at some point.
It would be straightforward to convert the three measurements from inches to centimeters by using:
1 inch = 2.54 cm
OR, we can make it easier on ourselves and calculate the volume in cubic inches, and then convert that to cubic centimeters. Then we just have one conversion to do, not three. So let's do that.
The volume of the ingot is:
10" x 4" x 3" = 120 in³
How do you convert that to cm³?
You use "1 in = 2.54 cm," but you cube each side:
(1 in)³ = (2.54 cm)³
1 in³ = 16.4 cm³
(I rounded to 3 significant figures, which is how precise the data is.)
Now you just multiply the volume by the conversion factor:
120 in³ x 16.4 cm³/in³ = 1968 cm³
Notice that in³ cancels out because it's in the top and the bottom.
Now that we know the volume of the gold, we multiply it by its density to get its mass. Notice again how the units work out:
1968 cm³ x 19.3 g/cm³ = 37,982 grams
But that's a lot of grams, so let's convert it to kilograms by dividing by 1000:
37,982 g ÷ 1000 g/kg = 40.0 kg