Gold has been a form of currency for centuries. To fool people into paying for a brick of gold without actually using pure gold, people have considered filling the centers of hollow gold bricks with lead. However, this does not work: Lead is a dense substance, but its density is not as great as that of gold, 19.3 g/cm3. What is the density of lead if a cube of lead has an edge length of 2.00 cm and a mass of 90.7 g? (5 points)
Question
Gold has been a form of currency for centuries. To fool people into paying for a brick of gold without actually using pure gold, people have considered filling the centers of hollow gold bricks with lead. However, this does not work: Lead is a dense substance, but its density is not as great as that of gold, 19.3 g/cm3. What is the density of lead if a cube of lead has an edge length of 2.00 cm and a mass of 90.7 g? (5 points)
Solution
To find the density of an object, you can use the formula:
Density = Mass / Volume
Given in the problem, we have:
Mass (m) = 90.7 g Edge length of the cube (a) = 2.00 cm
The volume (V) of a cube is given by the formula a³. So, the volume of the lead cube is:
V = a³ = (2.00 cm)³ = 8.00 cm³
Now we can find the density (D) using the formula:
D = m / V = 90.7 g / 8.00 cm³ = 11.34 g/cm³
So, the density of lead is 11.34 g/cm³.
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