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100pts!! 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. Please explain the clearest you can <3

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varshamittal029

Ellis will need 259.05 unit paint to paint all surfaces of 11 fenceposts.

What is the surface area of a cylinder ?

If, Radius of the cylinder be r and height of the cylinder be h,

Then, Surface area (A) = [tex]2\pi rh+2\pi r^{2}[/tex] sq. unit

How to find the amount of paint needed for Ellis ?

Ellis is painting wooden fenceposts which are of cylindrical shape.

The height of a fencepost (h) = 7 feet

The diameter of a fencepost = 1 foot

So, The radius of a fencepost (r) = [tex]\frac{1}{2}[/tex] foot

Given, the value of [tex]\pi[/tex] is 3.14

∴ Surface area of a fencepost (A) = [tex]2\pi rh+2\pi r^{2}[/tex]

                                                       = (2×3.14×[tex]\frac{1}{2}[/tex]×7)+(2×3.14×[tex](\frac{1}{2} )^{2}[/tex]) sq. feet

                                                       = (21.98+1.57) sq. feet

                                                       = 23.55 sq. feet

For 1 fencepost, Paint needed = 23.55 unit

For 11 fenceposts, Paint needed = 23.55×11 unit

                                                   = 259.05 unit

Hence, 259.05 unit paint needed for 11 fenceposts.

Learn more about surface area here :

https://brainly.com/question/27617975

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semsee45

Answer:

259.05 ft²

Step-by-step explanation:

Each fence post can be modeled as a cylinder.

Surface area of a cylinder

[tex]\sf SA=2 \pi r^2+2 \pi rh[/tex]

where:

  • r = radius
  • h = height

Given:

  • diameter = 1 ft ⇒ r = 0.5 ft
  • h = 7 ft
  • π = 3.14

Substitute the given values into the formula and solve for the surface area of one fence post:

[tex]\implies \sf SA=2 \cdot 3.14 \cdot (0.5)^2+2 \cdot 3.14 \cdot 0.5 \cdot 7[/tex]

[tex]\implies \sf SA = 1.57+21.98[/tex]

[tex]\implies \sf SA = 23.55\:\: ft^2[/tex]

Therefore, the surface area of 11 fence posts is:

= 11 × SA of one fence post

= 11 × 23.55

= 259.05 ft²

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