The perimeter of a minor sector of a circle of radius 4 units subtending an angle of 45° is:

To find the perimeter of a minor sector of a circle, we need to consider both the arc length and the two radii that form the sector.

Given:
- Radius \( r = 4 \) units
- Angle subtended by the sector \( \theta = 45^\circ \)

First, we need to convert the angle \(\theta\) from degrees to radians since the formula for the arc length uses radians.

\[
\theta_{\text{radians}} = \theta_{\text{degrees}} \times \frac{\pi}{180} = 45^\circ \times \frac{\pi}{180} = \frac{\pi}{4} \text{ radians}
\]

Next, we calculate the arc length \( L \) of the sector. The formula for the arc length \( L \) of a circle is:

\[
L = r \theta
\]

Substituting the given values:

\[
L = 4 \times \frac{\pi}{4} = \pi \text{ units}
\]

The perimeter \( P \) of the minor sector consists of the arc length plus the two radii:

\[
P = L + 2r
\]

Substituting the values we have:

\[
P = \pi + 2 \times 4 = \pi + 8 \text{ units}
\]

Thus, the perimeter of the minor sector of the circle is:

\[
\pi + 8 \text{ units}
\]

Would you like any further details or have any questions? Here are some related questions that might help deepen your understanding:

1. What is the difference between a minor sector and a major sector of a circle?
2. How do you convert degrees to radians and vice versa?
3. What is the formula for the area of a sector?
4. How does the perimeter of a sector change if the radius is doubled?
5. How do you find the length of the chord in a sector?
6. How would the problem change if the angle subtended was \( 90^\circ \)?
7. Can the perimeter of a sector be greater than the circumference of the circle?
8. What is the relationship between the arc length and the central angle?

**Tip**: When working with circles, always ensure angles are in radians if you are using formulas involving arc length or sector areas, as radians simplify the calculations.

Explore how to calculate the perimeter of a minor sector of a circle with radius 4 units and an angle of 45 degrees. Understand the arc length formula and its application in finding the sector's perimeter. Suitable for high school students learning about circles and arc lengths.

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