Arc Length and Area of Sectors - Practice Version

Front

What is the formula for the area of a sector?

Back

The area of a sector is given by the formula: \( A = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Front

What is the formula for arc length?

Back

The arc length is calculated using the formula: \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Front

Define 'arc length'.

Back

Arc length is the distance along a curved line, measured in linear units.

Front

What is the relationship between the radius and the area of a sector?

Back

The area of a sector increases with the square of the radius, as seen in the formula \( A = \frac{\theta}{360} \times \pi r^2 \).

Front

If a circle has a radius of 5 cm, what is the area of a sector with a central angle of 90°?

Back

Using the formula, the area is \( A = \frac{90}{360} \times \pi (5)^2 = \frac{1}{4} \times 25\pi = \frac{25\pi}{4} \) cm².

Front

How do you convert degrees to radians?

Back

To convert degrees to radians, use the formula: \( radians = degrees \times \frac{\pi}{180} \).

Front

What is the area of a sector with a radius of 6 inches and a central angle of 120°?

Back

Using the formula, the area is \( A = \frac{120}{360} \times \pi (6)^2 = \frac{1}{3} \times 36\pi = 12\pi \) in².

Front

What is the arc length of a circle with a radius of 10 m and a central angle of 45°?

Back

Using the formula, the arc length is \( L = \frac{45}{360} \times 2\pi (10) = \frac{1}{8} \times 20\pi = 2.5\pi \) m.

Front

What is the area of a sector with a radius of 8 cm and a central angle of 270°?

Back

Using the formula, the area is \( A = \frac{270}{360} \times \pi (8)^2 = \frac{3}{4} \times 64\pi = 48\pi \) cm².

Front

If the arc length is 15 cm and the radius is 5 cm, what is the central angle in degrees?

Back

Using the formula for arc length, \( L = \frac{\theta}{360} \times 2\pi r \), we can rearrange to find \( \theta = \frac{L \times 360}{2\pi r} = \frac{15 \times 360}{2\pi (5)} = \frac{10800}{10\pi} = \frac{1080}{\pi} \) degrees.