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)
Responses
a pipe with a radius of 16 inches and a height of 13 feet
a pipe with a radius of 16 inches and a height of 13 feet
a pipe with a radius of 9 inches and a height of 19 feet
a pipe with a radius of 9 inches and a height of 19 feet
a pipe with a radius of 18 inches and a height of 22 feet
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
To determine which cylinder could represent the given pipe, we first need to calculate the surface area of each cylinder using the formula for the surface area of a cylinder: 2πrh + 2πr^2.
a) Surface area = 2(3.14)(16 in)(13 ft) + 2(3.14)(16 in)^2 = 1601.28 ft^2
b) Surface area = 2(3.14)(9 in)(19 ft) + 2(3.14)(9 in)^2 = 1527.36 ft^2
c) Surface area = 2(3.14)(18 in)(22 ft) + 2(3.14)(18 in)^2 = 2173.04 ft^2
d) Surface area = 2(3.14)(36 in)(14 ft) + 2(3.14)(36 in)^2 = 2213.76 ft^2
Looking at the calculated surface areas, the cylinder that best represents the given pipe with a surface area of 221.37 ft^2 is option d) a pipe with a radius of 36 inches and a height of 14 feet.