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.

Answer 1

Answer:

244.92 ft^2

Step-by-step explanation:

Find out the surface area of 1 fence post.

It has 2 circular parts (a bottom and a top)

r = d / 2

r = 1 / 2

r = 0.5 feet.

Area = 3.14 * 0.5^2

area = 3.14 * 0.25

Area = 0.785

Each post has 2 such shapes. 2 * 0.785 = 1.57

There are 12 posts with areas of 1.57 on the bottom and top  = 18.84 ft^2

Find the area of the long part of the post

h = 6 feet

circumference = 2* pi * r

circumference = 2* 3.14 * .5

circumference = 3.14

The height is 6 feet.

The area of the body of the pole 6 *circumference = 6 * 3.14 = 18.84 ft^2

There are 12 poles.

Total area = 12 *18.84 ft^2 =  226.08

Total area = 12 bodies + 24 ends

Total area = 226.08 + 18.84

Total area = 244.92