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

Answer:

Silver

Step-by-step 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

$\sf \rho=\dfrac{m}{V}$

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:

$\implies \sf \rho=\dfrac{18.54}{0.5625 \pi}$

$\implies \sf \rho=10.49149385\:g\:cm^{-3}$

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.