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.

Question

Mathematics

Gordon Rogers

30 May, 17:36

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.

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Answers (1)

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Landen Pugh · Answer 1

Step-by-step explanation:

The fence posts are cylindrical. When painting all surfaces of the fence posts, we would calculate the amount of paint that would cover the total surface area of all the fence posts. The formula for determining the total surface area if a cylinder us expressed as

2πr² + 2πrh

Where

r represents radius of each fence post

h represents height of each fence post

From the information given,

diameter = 1 foot

Radius, r = diameter/2 = 1/2 = 0.5 foot

h = 6 feet

Total surface area = (2 * 3.14 * 0.5²) (2 * 3.14 * 0.5 * 6) = 20.41 ft²

Since there are 12 fenceposts in all, the paint must cover a total surface area of

20.41 * 12 = 244.92ft²