A plumber has a metal pipe with a surface area of 221.37 ft.2 . Which cylinder could represent this pipe? Use 3.14 to represent π .(1 point)
a pipe with a radius of 18 inches and a height of 22 feet
a pipe with a radius of 36 inches and a height of 14 feet
a pipe with a radius of 9 inches and a height of 19 feet
a pipe with a radius of 16 inches and a height of 13 feet
Let's use the formula for the surface area of a cylinder:
Surface Area = 2πrh + 2πr^2
First, we need to convert all the measurements to the same units. Since we are given the surface area in square feet, let's convert the radius and height measurements to feet:
1. Radius of 18 inches = 1.5 feet
2. Height of 22 feet = 22 feet
Now we can plug in the values and find the surface area for each cylinder:
1. Surface Area = 2π(1.5)(22) + 2π(1.5)^2 = 66π + 9π = 75π ≈ 235.62 ft^2 - This one is too large
2. Surface Area = 2π(3)(14) + 2π(3)^2 = 84π + 18π = 102π ≈ 320.04 ft^2 - This one is also too large
3. Surface Area = 2π(0.75)(19) + 2π(0.75)^2 = 28.5π + 1.125π = 29.625π ≈ 93.02 ft^2 - This one is too small
4. Surface Area = 2π(1.33)(13) + 2π(1.33)^2 = 34.58π + 17.68π = 52.26π ≈ 164.09 ft^2 - This pipe with a radius of 16 inches and a height of 13 feet is the closest match to the surface area of 221.37 ft^2 that the plumber has.