Areas Related to Circles — Sector & Segment

Sector

Meaning: A sector is a part of a circle between two radii and an arc.

Definition: Sector are$a = t$het$a / 360$ x $\pi$ $r^{2}$.

A $90-d$egree sector is on$e-f$ourth of a circle.

Arc Length

Meaning: Arc length is the curved length of a sector.

Definition: Arc lengt$h = t$het$a / 360$ x 2 $\pi$ r.

A $180-d$egree arc is half the circumference.

Segment

Meaning: A segment is the region between a chord and an arc.

Definition: Segment area can be found by subtracting triangle area from sector area.

For a minor segment, are$a = s$ector are$a - t$riangle area.

Major and Minor Parts

Meaning: Minor means smaller part and major means larger part.

Definition: A minor sector has angle less than 180 degrees. A major sector has angle greater than 180 degrees.

If a minor sector has angle 120 degrees, the major sector has angle 240 degrees.

• Major and minor parts together make the whole circle.

Easy

Question: Find the area of a $90-d$egree sector of radius 7 cm. Use $\pi$ = 22 / 7.

1. Sector are$a = 90 / 360$ x $\pi$ $r^{2}$.
2. Are$a = 1 / 4$ x $22 / 7$ x 7 x 7.
3. Are$a = 38$.5 c$m^{2}$.

Medium

Question: Find arc length of a $60-d$egree sector with radius 21 cm. Use $\pi$ = 22 / 7.

1. Arc lengt$h = 60 / 360$ x 2 $\pi$ r.
2. Ar$c = 1 / 6$ x 2 x $22 / 7$ x 21.
3. Ar$c = 22$ cm.

Exam-level

Question: A $90-d$egree sector of radius 14 cm contains a right triangle of area 98 c$m^{2}$. Find the segment area. Use $\pi$ = 22 / 7.

1. Sector are$a = 90 / 360$ x $22 / 7$ x 14 x $14 = 154$ c$m^{2}$.
2. Segment are$a = s$ector are$a - t$riangle area.
3. Segment are$a = 154 - 98 = 56$ c$m^{2}$.