Chapter 12.6, Problem 25STP

To determine

Calculate surface area of plastic cylindrical bar equivalent to metal bar.

Answer to Problem 25STP

Plastic cylindrical bar having radius 2 inch and height 0.5 inch has equal surface area that of metal cylindrical bar.

Explanation of Solution

Given:

Radius of metal bar= 1 inch

Height of metal bar=4 inch

Calculations:

Here, we have to calculate surface area of cylindrical bar and compare it with equivalent metal bar..

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

Firstly we will calculate surface area of metal bar,

$\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times 3.14\times 1^2)+(2\times 3.14\times 1\times 4)\\ =6.28+25.12\\ =31.4inc{h}^2\end{array}$

Now, we have to select appropriate dimensions of plastic cylindrical bar which is equal to surface area of metal cylindrical bar.

1. Radius 4 inch and height 2 inch:

$\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times 3.14\times 4^2)+(2\times 3.14\times 4\times 2)\\ =100.48+50.24\\ =150.72inc{h}^2\end{array}$

2. Radius 2 inch and height 2 inch:

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times 3.14\times 2^2)+(2\times 3.14\times 2\times 2)\\ =25.12+25.12\\ =50.24inc{h}^2\end{array}$

3. Radius 2 inch and height 4 inch:

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times 3.14\times 2^2)+(2\times 3.14\times 2\times 4)\\ =25.12+50.24\\ =75.36inc{h}^2\end{array}$

4. Radius 2 inch and 0.5 inch:

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times 3.14\times 2^2)+(2\times 3.14\times 2\times 0.5)\\ =25.12+6.28\\ =31.4inc{h}^2\end{array}$

Thus, from above findings radius 2 inch and height 0.5 inch results surface area equal to surface area of metal cylindrical bar.

Conclusion:

Therefore, we are able to calculate surface area of cylindrical bar using simple formula.