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
(1 point)
Responses
pipe D
pipe D
pipe B
pipe B
pipe A
pipe A
pipe C
pipe C
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To determine which pipe Lily should purchase, we need to calculate the surface area of each pipe.
Formula for the surface area of a cylinder: 2πr(r + h), where r is the radius and h is the height.
Let's calculate the surface area for each pipe:
Pipe A:
Radius = 0.50 feet
Height = 12 feet
Surface Area = 2 * 3.14 * 0.50(0.50 + 12) = 2 * 3.14 * 0.50 * 12.5 = 2 * 3.14 * 6.25 = 39.25 square feet
Pipe B:
Radius = 0.50 feet
Height = 16 feet
Surface Area = 2 * 3.14 * 0.50(0.50 + 16) = 2 * 3.14 * 0.50 * 16.5 = 2 * 3.14 * 8.25 = 51.78 square feet
Pipe C:
Radius = 0.75 feet
Height = 168 inches = 14 feet
Surface Area = 2 * 3.14 * 0.75(0.75 + 14) = 2 * 3.14 * 0.75 * 14.75 = 2 * 3.14 * 11.0625 = 69.56 square feet
Pipe D:
Radius = 0.25 feet
Height = 13 feet
Surface Area = 2 * 3.14 * 0.25(0.25 + 13) = 2 * 3.14 * 0.25 * 13.25 = 2 * 3.14 * 3.3125 = 20.78 square feet
Based on the calculations, Lily should purchase Pipe B as it has the closest surface area to 51.8 square feet that she needs.