Unit 5 Lesson 9 Circle Apply Sample Work

Answer 1

It seems you might be looking for assistance with a specific lesson or unit related to circles, possibly from a math curriculum. While I can't provide any specific "Unit 5 Lesson 9" directly, I can help explain concepts related to circles in geometry or apply relevant problems if that's what you need.

Here are some common concepts related to circles that might be part of a lesson:

Key Concepts about Circles

1. Radius: The distance from the center of the circle to any point on the circle.

2. Diameter: A line segment that passes through the center of the circle and has its endpoints on the circle. It is twice the length of the radius.

3. Circumference: The distance around the circle. The formula for calculating the circumference (C) is: \[ C = 2\pi r \quad \text{or} \quad C = \pi d \] where \( r \) is the radius, and \( d \) is the diameter.

4. Area: The space contained within the circle. The formula for calculating the area (A) is: \[ A = \pi r^2 \]

5. Chord: A line segment whose endpoints lie on the circle.

6. Arc: A portion of the circumference of a circle.

7. Sector: A region bounded by two radii and the arc between them.

Sample Problem

Problem: A circle has a radius of 3 cm. Calculate the circumference and area of the circle.

Solution:

1. Circumference: \[ C = 2\pi r = 2\pi(3) = 6\pi \approx 18.85 \text{ cm} \]

2. Area: \[ A = \pi r^2 = \pi(3^2) = 9\pi \approx 28.27 \text{ cm}^2 \]

Example Application

If you're studying the properties of circles and need to apply this knowledge, perhaps you’re working on a problem involving finding the length of an arc or the area of a sector.

Problem: Find the area of a sector that has a central angle of 60 degrees in a circle with a radius of 4 cm.

Solution:

• First, calculate the area of the entire circle. \[ A = \pi r^2 = \pi(4^2) = 16\pi \text{ cm}^2 \]

• Since the area of the sector is proportional to the central angle, the area of the sector (A_sector) can be calculated as: \[ A_{\text{sector}} = \frac{\theta}{360} \times A = \frac{60}{360} \times 16\pi = \frac{1}{6} \times 16\pi \approx 8.38 \text{ cm}^2 \]

If there are specific problems or different aspects you would like to explore regarding circles, please provide more details, and I'd be happy to assist!