Chapter 12.6, Problem 20HP

To determine

Calculate the effects of scale factor on surface area of cylinder.

Answer to Problem 20HP

Surface area of cylinder after scaling is four times smaller than original surface area of cylinder.

Explanation of Solution

Given:

Radius = 10 cm

Height =6 cm

Scale factor=0.5

Calculations:

Here, we have to calculate surface area 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

Putting values in equation, we get

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times \pi \times {10}^2)+(2\times \pi \times 10\times 6)\\ =628.31+376.99\\ =1005.30c{m}^2\end{array}$

When dimensions of cylinder are multiplied by scale factor, it affects the surface area of cylinder.

Surface area of cylinder after multiplying with scale factor 0.5,

Radius = 5 cm

Height = 3 cm

  $\begin{array}{l}Surfacearea=2\pi r^2+2\pi rh\\ =(2\times \pi \times 5^2)+(2\times \pi \times 5\times 3)\\ =157.07+94.24\\ =251.31c{m}^2\end{array}$

  $\begin{array}{l}$ {(Surfaceareaofcylinder)}_{original}={(Surfaceareaofcylinder)}_{scaled}$1005.30c{m}^2=251.31c{m}^2\\ \frac{1005.30c{m}^2}{251.31c{m}^2}=4.00\end{array}$

Surface area of cylinder after scaling is 4 times smaller than original surface area of cylinder.

Conclusion:

Therefore, we are able to calculate surface area of cylinder and effect of scaling on it.