Arc length and area of a sector worksheet answers – Embark on a journey through the captivating world of arc length and area of a sector with our comprehensive worksheet answers. Immerse yourself in the intricacies of this fascinating topic, as we unravel the formulas, explore real-world applications, and delve into the intricate relationship between arc length and central angle.
Prepare to expand your mathematical horizons and master the art of solving sector-related problems with ease.
Throughout this guide, we will provide a thorough understanding of the concepts, equip you with practical problem-solving techniques, and empower you to tackle any sector-related challenge with confidence. Let us begin our exploration into the realm of arc length and area of a sector, unlocking the secrets that lie within.
Arc Length and Area of a Sector: Arc Length And Area Of A Sector Worksheet Answers
In geometry, a sector is a region of a circle that is bounded by two radii and the intercepted arc. The arc length of a sector is the length of the intercepted arc, and the area of a sector is the area of the region bounded by the radii and the arc.
Arc Length, Arc length and area of a sector worksheet answers
The formula for calculating the arc length of a sector is:
$$s = r\theta$$
where:
- $s$ is the arc length
- $r$ is the radius of the circle
- $\theta$ is the central angle of the sector in radians
For example, if a sector has a radius of 5 cm and a central angle of 60 degrees, then the arc length of the sector is:
$$s = 5 cm – \frac60\pi180 \approx 5.24 cm$$
The arc length of a sector is directly proportional to the central angle of the sector. This means that the larger the central angle, the longer the arc length.
Area of a Sector
The formula for calculating the area of a sector is:
$$A = \frac12r^2\theta$$
where:
- $A$ is the area of the sector
- $r$ is the radius of the circle
- $\theta$ is the central angle of the sector in radians
For example, if a sector has a radius of 5 cm and a central angle of 60 degrees, then the area of the sector is:
$$A = \frac12 – 5 cm^2 – \frac60\pi180 \approx 13.09 cm^2$$
The area of a sector is directly proportional to the central angle of the sector. This means that the larger the central angle, the larger the area of the sector.
Worksheet Answers
Worksheet Problems:
- Find the arc length of a sector with a radius of 10 cm and a central angle of 120 degrees.
- Find the area of a sector with a radius of 6 cm and a central angle of 90 degrees.
Solutions:
- $$s = 10 cm
\frac120\pi180 = 20.94 cm$$
- $$A = \frac12
- 6 cm^2
- \frac90\pi180 = 9.42 cm^2$$
FAQ Compilation
What is the formula for calculating the arc length of a sector?
Arc length = (central angle/360) x 2πr
How do I find the area of a sector?
Area of sector = (central angle/360) x πr^2
What is the relationship between the arc length and the central angle of a sector?
The arc length of a sector is directly proportional to the central angle.
