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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.

Sagot :

semsee45

Answer:

Silver

Step-by-step explanation:

Find the volume of the coin

Volume of a cylinder

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

Given:

  • r = 1.5 cm
  • h = 0.25 cm

Substituting given values into the formula to find the volume:

[tex]\sf \implies V=\pi (1.5)^2(0.25)[/tex]

[tex]\sf \implies V=0.5625 \pi \:cm^3[/tex]

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

Density formula

[tex]\sf \rho=\dfrac{m}{V}[/tex]

where:

  • [tex]\rho[/tex] = density
  • m = mass
  • V = volume

Given:

  • m = 18.54 g
  • [tex]\sf V=0.5625 \pi \:cm^3[/tex]

Substituting given values into the density formula:

[tex]\implies \sf \rho=\dfrac{18.54}{0.5625 \pi}[/tex]

[tex]\implies \sf \rho=10.49149385\:g\:cm^{-3}[/tex]

Given:

  • [tex]\textsf{Density of Lead}=\sf 11.3\:g\:cm^{-3}[/tex]
  • [tex]\textsf{Density of Silver}=\sf 10.49\:g\:cm^{-3}[/tex]

Therefore, as [tex]\sf \rho=10.49\:g\:cm^{-3}[/tex] the coin is made from silver.

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