Explanation:
1 ft³ of gold will weigh 1209.6 pounds
1 ft³ of copper will weigh 559 pounds
We know the formula for:
Density = Mass/Volume
Hence, making mass the subject of the formula:
Mass = Density × Volume
From the question we are told:Volume of each metal = 1 ft³
1) Metal: Gold
Density of Gold = 0.70 pounds per cubic inch(lb/in³)
We convert the Volume of gold from ft³ to in³
The Volume of gold given in the question = 1 cubic foot = 1 ft³
1 cubic foot = 1728 cubic inches
Hence, the volume of Gold = 1728 in³
Mass of Gold = Density of Gold × Volume of Gold
Mass of Gold = 0.70Ib/in³ × 1728 in³
= 1209.6 lb(pounds)
2) Metal : Copper
Density of copper given in the question = 8.96 grams per cubic centimeter
Ib = pounds
We convert this density in g/cm³ to ib/in³
453.5g = 1 Ib
8.96g = a Ib
Cross Multiply
= 453.5g × a Ib =8.96g × 1 Ib
= a Ib = 8.96g × 1 Ib/453.5g
a Ib = 0.0197574421 Ib
Density of Copper = 0.0197574421 Ib/cm³
28,316.8 cm³ = 1 ft³
1 cm³ = b ft³
b ft³ = 1 cm³ × 1 ft³/28,316.8cm³
b ft³ = 0.0000353147 ft³
1 cm³ = 0.0000353147 ft³
We have to convert the density of Copper from Ib/cm³ to Ib/ft³
0.0197574421 Ib/cm³ = 0.0197574421 Ib/0.0000353147 ft³
559.46793026 Ib/ft³
Volume of copper = 1ft³
Mass = Density × Volume
Mass of copper = 559.46793026 Ib/ft³ × 1 ft³
= 559.46793026 Ib or pounds
≈ 559 pounds
Therefore , the weight of gold is 1209.6 pounds and the weight of copper will be 559 pounds.
