Question

Ellis is painting wooden fenceposts before putting them in his yard. They are each 5 feet tall and have a diameter of 1 foot. There are 10 fenceposts in all. How much paint will Ellis need to paint all the surfaces of the 10 fenceposts? Use 3.14 for it, and round your answer to the nearest hundredth. Provide an explanation and proof for your answer to receive full credit​

Answer 1

Answer:

39.25 cubic feet of paint will be needed by Ellis.

Step-by-step explanation:

Volume of a cylinder:

The volume of a cylinder of radius r and height h is given by:

$V = \pi r^2h = 3.14r^2h$

How much paint will Ellis need to paint all the surfaces of the 10 fenceposts?

This is the combined volume of these 10 fenceposts.

They are each 5 feet tall and have a diameter of 1 foot.

Radius is half the diameter, so $r = \frac{1}{2} = 0.5$. Also $h = 5$

10 fenceposts:

Each has the same volume, so:

$V = 10(3.14)r^2h = 31.4(0.5)^2(5) = 39.25$

39.25 cubic feet of paint will be needed by Ellis.