AOB is a sector of a circle, centre O - OCR - GCSE Maths - Question 23 - 2020 - Paper 1

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^2

where:

• 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^2

Simplifying the fraction:

rac{120}{360} = rac{1}{3}

This gives us:

8 = rac{1}{3} imes ext{π} r^2

Next, we can multiply both sides by 3 to isolate ( ext{π} r^2 ):

$$24 = ext{π} r^2$$

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}$$