How many pounds does 40.9 in3 of gold weigh? (The density of gold is 19.3 g/cm3, 2.54 cm = 1 in, and 454 g = 1 lb.)
Note these are not large volumes--a cup of water is about 30 in3.
So I tried this question and got 34.73, which isn't right. I used this: (1 in)3 = (2.54 cm)3
Path: in3 --> cm3 --> g --> lbs
can someone help please?
Why not show your work and let me find the error? It's easier that way for me to know what went wrong.
To find out how many pounds 40.9 in3 of gold weighs, you can follow these steps:
Step 1: Convert cubic inches (in3) to cubic centimeters (cm3)
Since there are 2.54 cm in 1 inch, you can use the conversion factor (2.54 cm)³ = (1 in)³ to convert in3 to cm3. Multiply 40.9 in3 by (2.54 cm)³ to get the volume in cm3.
40.9 in³ * (2.54 cm)³ = X cm³
Step 2: Convert cubic centimeters (cm3) to grams (g)
The density of gold is given as 19.3 g/cm3, which means that 19.3 grams of gold occupy 1 cubic centimeter of space. Use this conversion factor to convert the volume in cm3 to grams (g). Multiply the volume in cm3 by the density of gold, 19.3 g/cm³.
X cm³ * 19.3 g/cm³ = Y g
Step 3: Convert grams (g) to pounds (lbs)
Since 454 grams is equal to 1 pound, divide the weight in grams by 454 to convert to pounds.
Y g / 454 = Z lbs
The final result, Z, will be the weight of the gold in pounds.
Using these steps, let's calculate the weight of 40.9 in3 of gold:
Step 1: Convert cubic inches to cubic centimeters:
40.9 in³ * (2.54 cm)³ = 675.4294 cm³ (rounded to 6 decimal places)
Step 2: Convert cubic centimeters to grams:
675.4294 cm³ * 19.3 g/cm³ = 13,042.759 g (rounded to 3 decimal places)
Step 3: Convert grams to pounds:
13,042.759 g / 454 = 28.736 lbs (rounded to 3 decimal places)
Therefore, 40.9 in3 of gold weighs approximately 28.736 pounds.