Answered

Get the answers you need from a community of experts on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.

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 :

Semsee45idn

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.

Thank you for contributing to our discussion. Don't forget to check back for new answers. Keep asking, answering, and sharing useful information. Thank you for trusting IDNLearn.com. We’re dedicated to providing accurate answers, so visit us again for more solutions.