Final answer:
The length of the metal band needed to fasten sixteen pipes, each with a diameter of 10 cm, is 502.4 cm or roughly 5.024 m when calculated as the circumference of a circle formed by the arrangement of the pipes side by side.
Step-by-step explanation:
The question involves finding the length of a metal band that tightly fastens together sixteen pipes, each with a diameter of 10 cm. The length of the metal band is equivalent to the circumference of the circle formed by arranging the pipes side by side. The diameter of this arrangement will be equal to the diameter of one pipe multiplied by the number of pipes (since they are placed next to each other, touching).
Therefore, the total length of the band would be:
- The diameter of one pipe = 10 cm
- Total diameter = 10 cm x 16 = 160 cm
- Radius of the circle = Total diameter / 2 = 80 cm
- Circumference = 2 x π x radius = 2 x π x 80 cm
- Circumference = 160 x π cm (use π as approximately 3.14 for calculations)
The length of the metal band would therefore be 160 x 3.14 cm, which is roughly 502.4 cm or about 5.024 m.