A circle with a radius of 61cm is made from a wire.The wire is used to make a sector with a radius of 88cm.What is the angle sub

Question

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A circle with a radius of 61cm is made from a wire.The wire is used to make a sector with a radius of 88cm.What is the angle sub

tended by the sector?

Mathematics

1 answer:

olga55 [171] · Answer 1 · 2022-08-15T03:28:01+03:00

The circle has a radius of 61 cm, therefore its circumference is
C = 2π*61 = 122π cm

If the wire forms sector with a radius of 88 cm (as shown in the figure), then the length of the circular sector is
S = 122π - 2*88 = 207.2743 cm

Because the central angle is θ radians, therefore
88*θ = 207.2743
θ = 2.3554 radians
= (2.3554 rad)*(180 deg/rad)
= 134.95°

Answer:
The angle subtended by the sector is 135° (nearest whole number)