#4 Arc and sectors mini Flashcard

Front

What is the formula for the area of a sector?

Back

The area of a sector can be calculated using the formula: \( A = \frac{1}{2} r^2 \theta \), where \( r \) is the radius and \( \theta \) is the angle in radians.

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 formula for the arc length of a sector?

Back

The arc length \( L \) of a sector can be calculated using the formula: \( L = r \theta \), where \( r \) is the radius and \( \theta \) is the angle in radians.

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, meaning if the radius doubles, the area increases by a factor of four.

Front

What is the approximate value of \( \pi \)?

Back

The approximate value of \( \pi \) is 3.14.

Front

How do you find the perimeter of a sector?

Back

The perimeter of a sector can be found using the formula: \( P = 2r + L \), where \( L \) is the arc length.

Front

What is the significance of the angle in calculating the area of a sector?

Back

The angle determines the proportion of the circle that the sector represents; a larger angle results in a larger area.

Front

How do you calculate the area of a sector given the radius and angle in degrees?

Back

First, convert the angle from degrees to radians, then use the formula: \( A = \frac{1}{2} r^2 \theta \).

Front

What is the formula for the area of a circle?

Back

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

Front

What is the relationship between arc length and radius?

Back

The arc length is directly proportional to the radius; as the radius increases, the arc length increases for a given angle.