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.

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

c is the answer

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is