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To calculate the central angle \( \theta \) of sector \( OAB \), we use the formula for the area of a sector:

\[
\text{Area of sector} = \frac{1}{2} r^2 \theta
\]

Where:
- \( r \) is the radius (given as 4.3 mm),
- \( \theta \) is the central angle in radians,
- The area of sector \( OAB \) is given as 14 mm².

We rearrange the formula to solve for \( \theta \):

\[
\theta = \frac{2 \times \text{Area of sector}}{r^2}
\]

Substitute the known values:

\[
\theta = \frac{2 \times 14}{(4.3)^2}
\]

Now, let's calculate this value.The central angle \( \theta \) is approximately \( 1.51 \) radians to 1 decimal place.

Would you like further details or have any other questions? Here are some related questions you could explore:

1. How do you convert radians to degrees for central angles?
2. What is the formula for the circumference of a sector's arc?
3. How would the area change if the radius was doubled but the angle remained the same?
4. Can you calculate the length of arc \( AB \) in this sector?
5. How does the central angle affect the sector's area for a fixed radius?

**Tip:** When working with sectors, ensure you understand whether angles are provided in radians or degrees, as this affects calculations!

OAB is a sector of a circle. The area of OAB is 14 mm². Calculate the central angle θ, to 1 d.p. The radius is 4.3 mm.

Learn how to calculate the central angle of a sector, given the area and radius. This problem involves the formula for the area of a sector and solving for the central angle θ in radians. Example: Area = 14 mm², Radius = 4.3 mm.

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