Question

Sally finds a coin with a radius of 1.5 centimeters and a thickness of 0.25 cm. It has a measured mass of 18.54 grams. How can Sally use this to determine if the coin is made of Lead (density of 11.3 g/cubic centimeter) or Silver (10.49 g/cubic centimeter)? What is the coin made of? Explain.

Answer 1

Silver

Explanation:

Find the volume of the coin

Volume of a cylinder

`\textsf{V}=\sf \pi r^2 h \quad\textsf{(where r is the radius and h is the height)}`

Given:

• r = 1.5 cm
• h = 0.25 cm

Substituting given values into the formula to find the volume:

`\sf \implies V=\pi (1.5)^2(0.25)`

`\sf \implies V=0.5625 \pi \:cm^3`

Find the density of the coin given it has a measured mass of 18.54 g

Density formula

`\sf \rho=(m)/(V)`

where:

• 
  `\rho` = density
• m = mass
• V = volume

Given:

• m = 18.54 g
• 
  `\sf V=0.5625 \pi \:cm^3`

Substituting given values into the density formula:

`\implies \sf \rho=(18.54)/(0.5625 \pi)`

`\implies \sf \rho=10.49149385\:g\:cm^(-3)`

Given:

• 
  `\textsf{Density of Lead}=\sf 11.3\:g\:cm^(-3)`

• 
  `\textsf{Density of Silver}=\sf 10.49\:g\:cm^(-3)`

Therefore, as
`\sf \rho=10.49\:g\:cm^(-3)` the coin is made from silver.