Question

How do you derive the formula for the area of a sector?(1 point)
Responses

Divide the measurement of the sector’s angle by 360°
360
°
, then multiply the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 360 degrees , then multiply the quotient by pi times the radius squared.

Divide the measurement of the sector’s angle by 180°
180
°
, then multiply the quotient by π
𝜋
times the radius squared.
Divide the measurement of the sector’s angle by 180 degrees , then multiply the quotient by pi times the radius squared.

Divide the measurement of the sector’s angle by 360°
360
°
, then multiply the quotient by π
𝜋
times the radius.
Divide the measurement of the sector’s angle by 360 degrees , then multiply the quotient by pi times the radius.

Divide the measurement of the sector’s angle by 360°
360
°
, then divide the quotient by π
𝜋
times the radius squared.

Answer 1

Correct answer: Divide the sector’s angle by 360°, then multiply that fraction by π times the radius squared.

Derivation: A sector is a fraction of the whole circle equal to (angle/360). The whole circle’s area is πr^2, so sector area = (angle/360)·πr^2. (If the angle is in radians, area = (1/2)r^2·θ.)