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AOB is a sector of a circle, centre O - OCR - GCSE Maths - Question 24 - 2019 - Paper 1

Question 24

AOB is a sector of a circle, centre O. Show that the length of arc AB is 5.24 cm, correct to 3 significant figures.

Worked Solution & Example Answer:AOB is a sector of a circle, centre O - OCR - GCSE Maths - Question 24 - 2019 - Paper 1

Step 1

Step 1: Calculate the circumference of the circle

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Answer

The formula for the circumference of a circle is given by: $C = 2 \pi r$ where ( r ) is the radius of the circle. Here, the radius ( r ) is 6 cm. Thus, the circumference is:

$C = 2 \pi \times 6 = 12\pi \text{ cm} \approx 37.70 \text{ cm}$

Step 2

Step 2: Find the fraction of the circle represented by arc AB

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Answer

The angle for arc AB is 50 degrees. The fraction of the circle represented by this arc is:

$\frac{50}{360}$

Step 3

Step 3: Calculate the length of arc AB

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Answer

The length of arc AB can be calculated as: $\text{Length of arc AB} = \text{Fraction of circle} \times \text{Circumference}$ Substituting the values:

$\text{Length of arc AB} = \frac{50}{360} \times 12\pi \approx 5.236 \text{ cm}$ Rounding to 3 significant figures, we get:

$5.24 \text{ cm}$

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