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AOB is a sector of a circle, centre O - OCR - GCSE Maths - Question 23 - 2020 - Paper 1
Question 23
AOB is a sector of a circle, centre O. The area of the sector is 8 cm². Work out the exact value of the radius, r cm.
Worked Solution & Example Answer:AOB is a sector of a circle, centre O - OCR - GCSE Maths - Question 23 - 2020 - Paper 1
Step 1
Work out the exact value of the radius, r cm.
Answer
To find the radius of the sector, we can use the formula for the area of a sector:
ext{Area} = rac{ heta}{360} imes ext{π} r^2where:
- The area of the sector is given as 8 cm²,
- The angle ( \theta ) is 120°.
We will start by substituting the values into the formula:
8 = rac{120}{360} imes ext{π} r^2Simplifying the fraction:
rac{120}{360} = rac{1}{3}
This gives us:
8 = rac{1}{3} imes ext{π} r^2Next, we can multiply both sides by 3 to isolate ( ext{π} r^2 ):
Now, divide by π:
r^2 = rac{24}{ ext{π}}$$r = ext{√} rac{24}{ ext{π}}$$
Thus, the exact value of the radius ( r ) is:
r = rac{2 ext{√}6}{ ext{√} ext{π}} ext{ cm}$$