The density of gold is 19.3 g/cm^3. You inherit a gold bar that measures 7.0 inches by 3.0 inches by 2.0 inches. How many ounces does the bar weigh?
Show all work.
1 in = 2.54 cm
7.0 in x 3.0 in x 2.0 in = 42.0 in^3
42.0 in^3 x (2.54 cm/1 in)^3 = 5,845.3 cm^3
5,845.3 cm^3 x 19.3 g/cm^3 = 112,945.9 g
112,945.9 g x (1 oz/28.35 g) = 3,988.2 oz
To find the weight of the gold bar in ounces, we need to convert the volume of the bar from cubic inches to cubic centimeters, and then use the density of gold to find the weight. Here are the steps:
1. Convert the dimensions of the gold bar from inches to centimeters:
- Length: 7.0 inches x 2.54 cm/inch = 17.78 cm
- Width: 3.0 inches x 2.54 cm/inch = 7.62 cm
- Height: 2.0 inches x 2.54 cm/inch = 5.08 cm
2. Calculate the volume of the gold bar in cubic centimeters:
- Volume = Length x Width x Height = 17.78 cm x 7.62 cm x 5.08 cm = 693.25 cm³
3. Use the density of gold to calculate the weight in grams:
- Weight = Density x Volume = 19.3 g/cm³ x 693.25 cm³ = 13,392.43 g
4. Convert the weight from grams to ounces:
- 1 ounce = 28.3495 grams
- Weight in ounces = 13,392.43 g / 28.3495 g/oz = 472.73 oz (rounded to two decimal places)
Therefore, the gold bar weighs approximately 472.73 ounces.
To find the weight of the gold bar in ounces, we first need to calculate the volume of the bar in cubic centimeters. Then, we can use the density of gold to convert the volume to grams, and finally, convert grams to ounces.
Step 1: Calculate the volume of the gold bar in cubic centimeters.
Given:
Length = 7.0 inches
Width = 3.0 inches
Height = 2.0 inches
Convert the dimensions to centimeters:
1 inch = 2.54 cm
Length = 7.0 inches x 2.54 cm/inch = 17.78 cm
Width = 3.0 inches x 2.54 cm/inch = 7.62 cm
Height = 2.0 inches x 2.54 cm/inch = 5.08 cm
Volume = Length x Width x Height
= 17.78 cm x 7.62 cm x 5.08 cm
= 686.784 cm³
Step 2: Convert the volume from cubic centimeters to grams.
Given:
Density of gold = 19.3 g/cm³
Volume = 686.784 cm³
Mass = Density x Volume
= 19.3 g/cm³ x 686.784 cm³
≈ 13274.8992 g
Step 3: Convert the mass from grams to ounces.
Given:
1 ounce = 28.3495 grams
Weight (in ounces) = Mass (in grams) / 28.3495
= 13274.8992 g / 28.3495
≈ 468.53 ounces
Therefore, the gold bar weighs approximately 468.53 ounces.