Question

Find the distance to walk along the following path pls help I’m desperate

Answer 1

9514 1404 393

Answer:

• NQ = 3π units
• sector area = 9π square units
• 24 +3π units

Step-by-step explanation:

The formulas tell you for a circle of radius 6, ...

  C = 2π(6) = 12π

  A = πr² = π(6²) = 36π

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a)

Arc NQ is 1/4 of the circumference of the circle, so will have length ...

  NQ = 1/4C = 1/4(12π)

  NQ = 3π . . . . units

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b) Each sector is 1/4 the area of the circle. The area of one sector is ...

  sector area = 1/4A = 1/4(36π)

  sector area = 9π . . . . square units

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c) The total path length is equal to the sum of the lengths of the pieces of the path length. Each radius is 6 units.

PRQNP = PR +RQ +QN +NP

  = PR +RQ +QN +NR +RP

  = 6 +6 +3π +6 +6

path length = 24 +3π . . . . units

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Numerical answers (rounded to hundredths):

  NQ ≈ 9.42 u

  area ≈ 28.27 u²

  PRQNP = 33.42 u