Ellis is painting wooden fenceposts before putting them in his yard. They are each 7 feet tall and have a diameter of 1 foot. There are 11 fenceposts in all. How much paint will Ellis need to paint all the surfaces of the 11 fenceposts? Use 3.14 for π, and round your answer to the nearest hundredth. Provide an explanation and proof for your answer to receive full credit.

259.05 sq. ft.

Step-by-step explanation:

The quantity of paint used will be equal to the total surface area of the fence posts.

Since the wooden poles can be represented by closed cylinders geometrically, the Total Surface Area is

2πrh + 2πr^2

r = radius of post = 0.5 feet

T. S. A =

2 x 3.14 x 0.5 x 7 + 2 x 3.14 x 0.5^2

= 23.55 sq ft.

Since there are 11 fence posts, the total surface area will be multiplied by 11

= 23.55 x 11 = 259.05 sq. ft.

Therefore, the quantity of paint will be equal to the total surface area of the fence posts.