Lily needs to order a new pipe for her house. She needs the surface area of the pipe to be 51.8 square feet. The following pipes are all cylindrical and include closed, capped ends. If Lily can order any of the 3 pipes, which pipe should she purchase? Use 3.14 for π
pipe A: diameter of 0.50 feet, height of 12 feet
pipe B: radius of 0.50 feet, height of 16 feet
pipe C: radius of 0.75 feet, height of 168 inches
pipe D: diameter of 0.25 feet, height of 13 feet
To determine which pipe Lily should purchase, we need to calculate the surface area of each pipe and see which one is closest to 51.8 square feet.
Let's start by calculating the surface area of each pipe:
Pipe A:
Radius = 0.25 feet (half of the diameter)
Height = 12 feet
Surface Area = 2πr(r+h)
Surface Area = 2(3.14)(0.25)(0.25+12)
Surface Area = 2(3.14)(0.25)(12.25)
Surface Area = 2(3.14)(0.25)(12.25)
Surface Area = 2(3.14)(0.25)(12.25)
Surface Area = 48.11 square feet
Pipe B:
Radius = 0.50 feet
Height = 16 feet
Surface Area = 2πrh + 2πr^2
Surface Area = 2(3.14)(0.50)(16) + 2(3.14)(0.50)^2
Surface Area = 2(3.14)(0.50)(16) + 2(3.14)(0.25)
Surface Area = 2(3.14)(0.50)(16) + 2(3.14)(0.25)
Surface Area = 50.24 square feet
Pipe C:
Radius = 0.75 feet
Height = 168 inches = 14 feet
Surface Area = 2πrh + 2πr^2
Surface Area = 2(3.14)(0.75)(14) + 2(3.14)(0.75)^2
Surface Area = 2(3.14)(0.75)(14) + 2(3.14)(0.56)
Surface Area = 2(3.14)(0.75)(14) + 2(3.14)(0.56)
Surface Area = 48.85 square feet
Pipe D:
Radius = 0.125 feet (half of the diameter)
Height = 13 feet
Surface Area = 2πr(r+h)
Surface Area = 2(3.14)(0.125)(0.125+13)
Surface Area = 2(3.14)(0.125)(13.125)
Surface Area = 2(3.14)(0.125)(13.125)
Surface Area = 1.03 square feet
Based on the calculations, Lily should purchase Pipe B as its surface area is closest to 51.8 square feet (48.11 < 51.8 < 50.24 < 48.85).