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?
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.
To determine the number of gallons of water that have the same mass as the given bar of gold, we need to follow these steps:
Step 1: Calculate the volume of the gold bar.
The volume of the gold bar can be calculated by multiplying its length, width, and height:
Volume = 0.15 m × 0.050 m × 0.050 m
Step 2: Convert the volume from cubic meters to liters.
There are 1000 liters in one cubic meter. So, to convert cubic meters to liters, we multiply the volume by 1000:
Volume (liters) = Volume (cubic meters) × 1000
Step 3: Convert the volume from liters to gallons.
There are approximately 3.78541 liters in one gallon. So, to convert liters to gallons, we divide the volume in liters by 3.78541:
Volume (gallons) = Volume (liters) / 3.78541
Step 4: Calculate the mass of the gold bar.
Assuming the density of gold is 19.32 grams per cubic centimeter, we can calculate the mass of the gold bar by multiplying its volume by the density. However, we need to convert the units:
Density of gold (g/cm³) = 19.32 g/cm³
Volume (cm³) = Volume (liters) × 1000 (since 1 liter = 1000 cm³)
Mass (grams) = Volume (cm³) × Density (g/cm³)
Step 5: Convert the mass from grams to pounds.
There are approximately 0.00220462 pounds in one gram. So, to convert grams to pounds, we divide the mass in grams by 453.592:
Mass (pounds) = Mass (grams) / 453.592
Step 6: Calculate the density of water.
The density of water is approximately 1 gram per cubic centimeter.
Step 7: Calculate the volume of water with the same mass.
To find the volume of water that has the same mass as the gold bar, we divide the mass of the gold bar (in grams) by the density of water (in grams per cubic centimeter):
Volume of water (cm³) = Mass of gold (grams) / Density of water (g/cm³)
Step 8: Convert the volume from cubic centimeters to gallons.
To convert the volume from cubic centimeters to gallons, we divide the volume in cubic centimeters by 3785.41 (since 1 gallon = 3785.41 cm³):
Volume of water (gallons) = Volume of water (cm³) / 3785.41
By following these steps, we can determine the number of gallons of water that have the same mass as the given bar of gold.
To determine the number of gallons of water that have the same mass as the given bar of gold, we need to follow a series of steps:
Step 1: Find the volume of the gold bar.
To calculate the volume, multiply the length, width, and height of the gold bar together:
Volume of gold bar = 0.15 m * 0.050 m * 0.050 m
Step 2: Convert the volume from cubic meters to liters.
Since there are 1000 liters in 1 cubic meter, multiply the volume by 1000 to convert it to liters:
Volume in liters = Volume of gold bar * 1000
Step 3: Convert the volume from liters to gallons.
Since there are 3.78541 liters in 1 gallon, divide the volume in liters by 3.78541 to convert it to gallons:
Volume in gallons = Volume in liters / 3.78541
Step 4: Convert the mass of the gold bar to water.
Water has a density of 1000 kg/m³, and we need to convert the mass of the gold bar to kilograms to match the density. Assume the density of gold is 19,320 kg/m³ (typical for gold). Multiply the volume of the gold bar by its density to get the mass:
Mass of gold bar = Volume of gold bar * density of gold
Step 5: Convert the mass from kilograms to grams.
Multiply the mass by 1000 to convert it from kilograms to grams:
Mass of gold bar in grams = Mass of gold bar * 1000
Step 6: Convert the mass from grams to gallons of water.
Since there are 454 grams in 1 pound and 8.3454 pounds in 1 gallon of water, divide the mass in grams by 454 and then divide again by 8.3454 to get the number of gallons of water:
Number of gallons of water = Mass of gold bar in grams / (454 g/pound * 8.3454 pound/gallon)
By following these steps, you will find the answer to your question, "How many gallons of water have the same mass as this bar?"