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
To determine which pipe Lily should purchase, we need to calculate the surface area of each of the three pipes and compare it to the required 51.8 square feet.
1. Pipe A:
- Radius = 3 feet
- Length = 6 feet
Surface Area = 2πrh + 2πr^2
= 2 * 3.14 * 3 * 6 + 2 * 3.14 * 3^2
= 113.04 + 56.52
= 169.56 square feet
2. Pipe B:
- Radius = 2 feet
- Length = 12 feet
Surface Area = 2πrh + 2πr^2
= 2 * 3.14 * 2 * 12 + 2 * 3.14 * 2^2
= 150.72 + 25.12
= 175.84 square feet
3. Pipe C:
- Radius = 4 feet
- Length = 4 feet
Surface Area = 2πrh + 2πr^2
= 2 * 3.14 * 4 * 4 + 2 * 3.14 * 4^2
= 100.48 + 100.48
= 200.96 square feet
Comparing the surface areas:
- Pipe A: 169.56 square feet
- Pipe B: 175.84 square feet
- Pipe C: 200.96 square feet
Based on the calculations, Lily should purchase Pipe A as it has the closest surface area to the required 51.8 square feet.