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

The perimeter of a sector of a circle consists of two parts: the length of the arc and the two radii.

### Formula for the perimeter of a sector:
\[
P = 2r + \text{Arc Length}
\]
Where:
- \( r \) is the radius of the circle.
- Arc Length is given by:
\[
\text{Arc Length} = \theta \times r
\]
where \( \theta \) is the central angle in radians.

To find the perimeter of the minor sector with:
- Radius \( r = 4 \) units.
- Central angle \( \theta = 45^\circ \).

#### Step 1: Convert the angle from degrees to radians
\[
\theta = 45^\circ = \frac{45 \pi}{180} = \frac{\pi}{4} \text{ radians}
\]

#### Step 2: Calculate the arc length
\[
\text{Arc Length} = \frac{\pi}{4} \times 4 = \pi \text{ units}
\]

#### Step 3: Calculate the perimeter
\[
P = 2r + \text{Arc Length} = 2 \times 4 + \pi = 8 + \pi \text{ units}
\]

Thus, the perimeter of the minor sector is:
\[
P = 8 + \pi \text{ units}
\]

Would you like further details or have any questions?

---

Here are 5 related questions you might find interesting:
1. How does the perimeter of a sector change with a different central angle?
2. What is the area of this same minor sector?
3. How do you convert between radians and degrees?
4. How do you calculate the arc length if the angle is given in radians?
5. What happens to the perimeter if the radius is doubled?

**Tip:** Remember that angles in radians are often easier to work with when dealing with sectors in calculus and trigonometry.

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

Calculate the perimeter of a minor sector of a circle with radius 4 units and an angle of 45°. Learn how to convert the angle from degrees to radians and apply the formula for the perimeter. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation