Question

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.

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 lateral - surface area of one fence - post

The formula for the lateral - surface area of a cylinder $A_{l}=2\pi rh$. Substituting $r = 0.5$ foot, $h = 7$ feet and $\pi=3.14$, we get $A_{l}=2\times3.14\times0.5\times7=21.98$ square feet.

Step3: Calculate the area of the two circular ends of one fence - post

The formula for the area of a circle is $A_{c}=\pi r^{2}$. The area of two circular ends $A_{2c}=2\times\pi r^{2}$. Substituting $r = 0.5$ foot and $\pi = 3.14$, we get $A_{2c}=2\times3.14\times(0.5)^{2}=1.57$ square feet.

Step4: Calculate the total surface area of one fence - post

The total surface area of one fence - post $A = A_{l}+A_{2c}=21.98 + 1.57=23.55$ square feet.

Step5: Calculate the total surface area of 11 fence - posts

The total surface area of 11 fence - posts $A_{total}=11\times A$. Substituting $A = 23.55$ square feet, we get $A_{total}=11\times23.55 = 259.05$ square feet.

Answer:

259.05 square feet