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Zorluk: OrtaCircular Area and Circumference Applications

An industrial steel cable is wrapped around a cylindrical hoisting drum that has a diameter of 2.52.5 feet. If the drum must complete exactly 4040 full rotations to completely unwind the cable, what is the total length of the cable? (Use π=3.14\pi = 3.14)

  1. A
    7.857.85 feet
  2. B
    196.25196.25 feet
  3. 314314 feetCevap
  4. D
    628628 feet

Cevap

The total length of the cable is 314314 feet.
The length of cable unwound in one rotation is exactly equal to the circumference of the drum. Using the formula C=π×dC = \pi \times d, the circumference is 3.14×2.5=7.853.14 \times 2.5 = 7.85 feet. Since the drum rotates 4040 times, the total cable length is 7.85 feet/rotation×40 rotations=3147.85 \text{ feet/rotation} \times 40 \text{ rotations} = 314 feet.

Adım Adım Çözüm

1
Calculate the circumference of the cylindrical drum.
C=π×d=3.14×2.5=7.85C = \pi \times d = 3.14 \times 2.5 = 7.85 feet.
One full rotation of the drum unwinds an amount of cable equal to the drum's circumference.
2
Multiply the circumference by the number of rotations to find the total length.
7.85×40=3147.85 \times 40 = 314 feet.
The drum completes 4040 rotations, meaning 4040 lengths of the circumference are unwound.

Anahtar Kavram

Distance from Rotations (Circumference)
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Konular

Circular Area and Circumference Applications

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