Question

beth has been hired to paint vistaville city hall, which has six large, cylindrical pillars in its entryway that reach from floor to ceiling. each pillar is 19 feet tall with a radius of 2 feet. what is the total area of the pillars that beth will paint? round your answer to the nearest hundredth. square feet

Explanation:

Step1: Find the lateral surface area of one pillar

The formula for the lateral surface area of a cylinder is \(A = 2\pi rh\). Given \(r = 2\) feet and \(h=19\) feet.

$$A_1=2\pi\times2\times19$$

$$A_1 = 76\pi$$

Step2: Calculate the total lateral surface area of six pillars

Since there are \(n = 6\) pillars, the total area \(A_{total}=n\times A_1\)

$$A_{total}=6\times76\pi$$

$$A_{total}=456\pi$$

Using \(\pi\approx3.14159\)

$$A_{total}=456\times3.14159$$

$$A_{total}=1422.56404$$

Answer:

\(1422.56\) square feet