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Math  /  Geometry

QuestionOAB is a sector of a circle as shown below.
Work out the length of the arc AB . Give your answer to 1 d.p.

Studdy Solution

STEP 1

1. The sector OAB is part of a circle with center O O .
2. The angle ∠AOB \angle AOB is 62∘ 62^\circ .
3. The radius of the circle is 43 43 mm.

STEP 2

1. Recall the formula for the length of an arc.
2. Substitute the given values.
3. Calculate the arc length.
4. Round the answer to 1 decimal place.

STEP 3

Recall the formula for the length of an arc:
Arc Length=θ360∘×2πr \text{Arc Length} = \frac{\theta}{360^\circ} \times 2\pi r
where θ \theta is the central angle in degrees, and r r is the radius.

STEP 4

Substitute the given values into the formula:
Arc Length=62∘360∘×2π×43 mm \text{Arc Length} = \frac{62^\circ}{360^\circ} \times 2\pi \times 43 \text{ mm}

STEP 5

Calculate the arc length:
Arc Length=62360×2π×43 \text{Arc Length} = \frac{62}{360} \times 2\pi \times 43 ≈0.1722×2π×43 \approx 0.1722 \times 2\pi \times 43 ≈0.1722×269.8 \approx 0.1722 \times 269.8 ≈46.44 mm \approx 46.44 \text{ mm}

STEP 6

Round the answer to 1 decimal place:
Arc Length≈46.4 mm \text{Arc Length} \approx 46.4 \text{ mm}
The length of the arc AB is:
46.4 mm \boxed{46.4 \text{ mm}}

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