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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
