Question

the density of gold is 19.3 g/cm^3. You inherit a gold bar that measures 7.0 in by 3.0 in by 2.0 in. How many ounces does the bar weigh? Express answer in scientific notation.

Answer 1

To find the weight of the gold bar, we need to calculate its volume and use the density of gold. The gold bar weighs approximately 467.96 ounces.

Step-by-step explanation:

To find the weight of the gold bar in ounces, we first need to calculate its volume in cubic inches and then convert it to cubic centimeters.

Given:

• Length = 7.0 inches
• Width = 3.0 inches
• Height = 2.0 inches

The volume (V) of a rectangular prism is given by V = Length x Width x Height.

V = 7.0 in x 3.0 in x 2.0 in = 42.0 in³

Since 1 inch is equal to 2.54 centimeters, we can convert the volume to cubic centimeters:

V = 42.0 in³ x (2.54 cm/in)³ = 686.98 cm³

Now, to find the weight of the gold bar in ounces, we can use the density of gold, which is 19.3 g/cm³.

The formula for density is Density = Mass/Volume.

Since we know the density and the volume, we can rearrange the formula to solve for the mass:

Mass = Density x Volume

Mass = 19.3 g/cm³ x 686.98 cm³ = 13,257.814 g

Finally, to convert the mass from grams to ounces, we divide by 28.35 grams/ounce:

Weight in ounces = 13,257.814 g / 28.35 g/oz = 467.96 oz

Therefore, the gold bar weighs approximately 467.96 ounces.

Answer 2

You can work out the following: Mass = Density x Volume Density = Mass Ă· Volume Volume = Mass Ă· Density The density of gold is 0.670205 oz/cm^3 The volume is length x width x depth = 7*3*2 = 42 The answer is Mass = 0.670205 x 42 = 281 ounces