Question

ellis is painting wooden fenceposts before putting them in his yard. they are each 6 feet tall and have a diameter of 1 foot. there are 12 fenceposts in all. how much paint will ellis need to paint all the surfaces of the 12 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.

Explanation:

Step1: Calculate the radius of the fence - post

The diameter $d = 1$ foot, so the radius $r=\frac{d}{2}=\frac{1}{2}=0.5$ foot.

Step2: Calculate the surface - area of one fence - post

A fence - post is a cylinder. The surface - area formula of a cylinder is $A = 2\pi r^{2}+2\pi rh$.
The two circular ends have an area of $2\pi r^{2}=2\times3.14\times0.5^{2}=2\times3.14\times0.25 = 1.57$ square feet.
The lateral surface area is $2\pi rh=2\times3.14\times0.5\times6=18.84$ square feet.
So the total surface - area of one fence - post is $A=1.57 + 18.84=20.41$ square feet.

Step3: Calculate the total surface - area of 12 fence - posts

Multiply the surface - area of one fence - post by 12. So the total surface - area $=20.41\times12 = 244.92$ square feet.

Answer:

244.92 square feet