Chapter 12.6, Problem 12PPS

To determine

Calculate the surface area of pillar that needs more painting.

Answer to Problem 12PPS

Taryn will need more paint for pillar2 as surface area of pillar 2 is more than pillar 1.

Explanation of Solution

Given:

For pillar 1: Diameter=0.15 m ; Radius=0.075m

Height = 0.75m

For pillar 2: Diameter=0.30 m ; Radius=0.15m

Height = 0.38m

Calculations:

Here, we have to calculate surface area of cylinder.

We know that, surface area of pillar 1 is calculated as,

  $Surfacearea=2\pi r_1{}^2+2\pi r_{1}h$

Where, $r_1$ is the radius of pillar 1

h is the height of pillar 1

Putting values in equation, we get

  $\begin{array}{l}Surfacearea=2\pi r_1{}^2+2\pi r_{1}h\\ =(2\times \pi \times {0.075}^2)+(2\times \pi \times 0.075\times 0.75)\\ =0.03534+0.3534\\ =0.3887m^2\end{array}$

Similarly we can calculate surface area of pillar 2,

  $Surfacearea=2\pi r_2{}^2+2\pi r_{2}h$

Where, $r_2$ is the radius of pillar 1

h is the height of pillar 1

Putting values, we get

  $\begin{array}{l}Surfacearea=2\pi r_2{}^2+2\pi r_{2}h\\ =(2\times \pi \times {0.15}^2)+(2\times \pi \times 0.15\times 0.38)\\ =0.1413+0.3581\\ =0.4994m^2\end{array}$

As the surface area of pillar2 is larger than that of pillar1, thus Taryn will need more paint for pillar2.

Conclusion:

Therefore, we are able to calculate surface area of both pillars and can conclude that pillar 2 will require more paint than pillar 1.