A bar of gold measures 0.15 m × 0.050 m × 0.050 m. How many gallons of water have the same mass as this bar?

Answer 1

To find the mass of the gold bar, we need to use the formula:

mass = volume x density,

where volume = length x width x height, and density of gold is approximately 19.32 g/cm³.

The gold bar has a volume of:
0.15 m × 0.050 m × 0.050 m = 0.000375 m³

To convert this volume to cm³, we multiply by (100 cm/m)^3:
0.000375 m³ * (100 cm/m)^3 = 375 cm³

Now, we'll find the mass of the gold bar by multiplying its volume by its density:
375 cm³ * 19.32 g/cm³ = 7245 g

Now, we want to find out the volume of water that has the same mass as the gold bar we calculated. To do this, we divide the mass of the gold by the density of water, which is 1 g/cm³:

7245 g ÷ 1 g/cm³ = 7245 cm³

Now let's convert cm³ to gallons. We know that:
1 gallon = 3.78541 liters and 1 liter = 1000 cm³, so:

1 gallon = 3.78541 L × 1000 cm³/L = 3785.41 cm³

Now we find out how many gallons of water have the same mass as the gold bar:

7245 cm³ ÷ 3785.41 cm³/gallon ≈ 1.91 gallons

So, about 1.91 gallons of water have the same mass as the gold bar.