The diagram shows a sector OAB of a circle with centre O and radius 2 - AQA - A-Level Maths: Mechanics - Question 3 - 2020 - Paper 1
Question 3
The diagram shows a sector OAB of a circle with centre O and radius 2.
The angle AOB is θ radians and the perimeter of the sector is 6.
Find the value of θ.
Circle y... show full transcript
Worked Solution & Example Answer:The diagram shows a sector OAB of a circle with centre O and radius 2 - AQA - A-Level Maths: Mechanics - Question 3 - 2020 - Paper 1
Step 1
Find the formula for the perimeter of a sector
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Answer
The perimeter of a sector is given by the formula:
[ P = r \theta + 2r ]\ where:
(P) is the perimeter of the sector,
(r) is the radius of the circle,
(\theta) is the angle in radians.
Step 2
Substitute known values into the formula
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Answer
We know that the radius (r = 2) and the perimeter (P = 6).
Substituting these values into the formula gives us:
[ 6 = 2 \theta + 2 \times 2 ]\
This simplifies to:
[ 6 = 2 \theta + 4 ]
Step 3
Solve for θ
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Answer
Rearranging the equation to isolate (\theta):
[ 6 - 4 = 2\theta]\
[ 2 = 2\theta]\
Dividing both sides by 2 yields:
[ \theta = 1 ]
Step 4
Circle your answer
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Answer
The value of (\theta) is 1. Circle this answer as instructed.
