Arc Length and Sector Area

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 the length of an arc?

Back

The length of an arc is given by 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' in the context of a circle.

Back

An arc is a portion of the circumference of a circle.

Front

What is the relationship between the radius and the circumference of a circle?

Back

The circumference of a circle is calculated using the formula: \( C = 2\pi r \), where \( r \) is the radius.

Front

If the radius of a circle is 5 inches, what is the circumference?

Back

Using the formula \( C = 2\pi r \), the circumference is \( C = 2\pi(5) = 10\pi \) inches.

Front

What does the term 'sector' refer to in a circle?

Back

A sector is a region enclosed by two radii and the arc between them.

Front

How do you calculate the area of a circle?

Back

The area of a circle is calculated using the formula: \( A = \pi r^2 \), where \( r \) is the radius.

Front

What is the angle in degrees for a full circle?

Back

The angle in degrees for a full circle is 360 degrees.

Front

If a sector has an angle of 90 degrees and a radius of 4 cm, what is its area?

Back

Using the formula \( A = \frac{\theta}{360} \times \pi r^2 \), the area is \( A = \frac{90}{360} \times \pi (4^2) = \frac{1}{4} \times 16\pi = 4\pi \) cm².

Front

What is the length of an arc with a radius of 3 m and an angle of 60 degrees?

Back

Using the formula \( L = \frac{\theta}{360} \times 2\pi r \), the length is \( L = \frac{60}{360} \times 2\pi(3) = \frac{1}{6} \times 6\pi = \pi \) m.