Question 1

What is the formula for the area of a sector?

Accepted Answer

In degrees, the area of a sector is S = (n / 360) * π * r², or S = 1/2 * l * r where l is arc length. In radians, S = 1/2 * θ * r².

Question 2

What is the formula for the arc length of a circle?

Accepted Answer

In degrees, arc length is l = (n / 180) * π * r because the factor of 2 in 2πr cancels with 360. In radians, l = θ * r.

Question 3

Why is arc length divided by 180 while sector area is divided by 360?

Accepted Answer

Circle circumference has 2 (2πr), canceling 360 to 180. Circle area is πr² with no factor 2, keeping 360 intact.

Question 4

How to calculate the perimeter of a sector?

Accepted Answer

The perimeter of a sector is C = l + 2r, which includes the curved arc length l plus the two straight radii 2r.