Chapter 12.6, Problem 16PPS

To determine

Calculate ratio between the surface areas of penny and nickel

Answer to Problem 16PPS

Ratio between the surface areas of penny and nickel is 0.792

Explanation of Solution

Given:

  $Penny’smass=\frac{Nickelmass}{2}$

Coin	Penny	Nickel
Mass	2.5g	5 g
Diameter	19.05 mm	21.21 mm
Radius	9.525 mm	10.605 mm
Thickness	1.55mm	1.95 mm

Calculations:

Here, we have to calculate surface area of cylinder, as coins are in the shape of cylinder.

We know that, surface area of cylinder is calculated as,

  $Surfacearea=2\pi r^2+2\pi rh$

Where, r is the radius of cylinder

h is the height of cylinder

First, we will calculate surface area of Penny,

  $\begin{array}{l}SurfaceareaofPenny=2\pi r^2+2\pi rh\\ =(2\times 3.14\times {9.525}^2)+(2\times 3.14\times 9.525\times 1.55)\\ =569.75+92.716\\ =662.466m{m}^2\end{array}$

Now, surface area of nickel is

  $\begin{array}{l}SurfaceareaofNickel=2\pi r^2+2\pi rh\\ =(2\times 3.14\times {10.605}^2)+(2\times 3.14\times 10.605\times 1.95)\\ =706.286+129.868\\ =836.154m{m}^2\end{array}$

Ratio of surface area of penny and Nickel are,

  $\frac{Surfaceareaofpenny}{Surfaceareaofnickel}=\frac{662.466}{836.154}=0.792$

Conclusion:

Therefore, we are able to calculate ratio of surface areas of two different metals using simple formula.