geometry study guide

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 to the nearest hundredth for final answer

Answer 1

This problem is asking you to find the total surface area of the 12 fenceposts. To calculate the surface area of a 3-D object, add the areas of the faces of the shape. Here, the fenceposts are cylinders. Find the surface area of one fencepost and multiply the result by 12.

To visualize a cylinder's surfaces, consider a can of soup. The surfaces of a can of soup consist of two circles and a rectangle. One circle on top, one circle on the bottom, and the rectangle is the label from the can of soup.

"SURFACE AREA OF CYLINDER = CIRCLE AREA + CIRCLE AREA + RECTANGLE AREA"

The fencepost (cylinder) has given dimensions:

height = 6 ft.

diameter = 1 ft.

radius = 0.5 ft. (radius is half of the diameter)

Area of circle = πr² , where π ≈ 3.14

CIRCLE AREA = 3.14(0.5)² sq. ft.

= 3.14(0.25) sq. ft.

= 0.785 sq. ft.

Area of rectangle = circumference × height

This rectangle's base is the circumference of the circle and the height is the height of the fencepost.

Circumference = diameter × π = 1 ft. × 3.14

RECTANGLE AREA = 3.14(6) sq. ft.

= 18.84 sq. ft.

"SURFACE AREA OF CYLINDER = CIRCLE AREA + CIRCLE AREA + RECTANGLE AREA"

Surface area of one fencepost = (0.785 + 0.785 + 28.84) sq. ft.

= 20.41 sq. ft.

Surface area of 12 fenceposts = 12 × 20.41 sq. ft.

244.92 sq. ft.

Thus, you need enough paint to cover 244.92 sq. ft. (For reference, 1 gallon of paint covers about 400 sq. ft.)