VT · Arc Length & Sector Area

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In each set, one thing changes and everything else stays the same. Work them out in order and look for the pattern — the last line tells you what to notice.

①Sector area — the angle stays 90°, the radius changeschanging: radius
Work out the area of each sector.
4 cm
Sector (not to scale)90°4 cm
=
6 cm
Sector (not to scale)90°6 cm
=
8 cm
Sector (not to scale)90°8 cm
=
10 cm
Sector (not to scale)90°10 cm
=
What happens to the area each time the radius goes up? What about when it doubles?
②Sector area — the radius stays 12 cm, the angle changeschanging: angle
Work out the area of each sector.
45°
Sector (not to scale)45°12 cm
=
90°
Sector (not to scale)90°12 cm
=
135°
Sector (not to scale)135°12 cm
=
180°
Sector (not to scale)180°12 cm
=
The angle doubles from 45° to 90° to 180°. What happens to the area?
③Arc length — the angle stays 120°, the radius changeschanging: radius
Work out the length of the arc of each sector.
3 cm
Sector (not to scale)120°3 cm
=
6 cm
Sector (not to scale)120°6 cm
=
9 cm
Sector (not to scale)120°9 cm
=
12 cm
Sector (not to scale)120°12 cm
=
How is the arc length changing compared with the radius?
④Same sector (radius 8 cm, angle 90°) — what changes is what you are asked to findchanging: what to find
For this one sector, work out:
the arc length
Sector (not to scale)90°8 cm
=
the area
Sector (not to scale)90°8 cm
=
the perimeter
Sector (not to scale)90°8 cm
=
Same numbers, three different formulas. Which parts of the working are the same?

Answers · Arc Length & Sector Area

Variation practice
① Sector area — the angle stays 90°, the radius changes
4 cm: 12.6 cm²6 cm: 28.3 cm²8 cm: 50.3 cm²10 cm: 78.5 cm²
② Sector area — the radius stays 12 cm, the angle changes
45°: 56.5 cm²90°: 113 cm²135°: 170 cm²180°: 226 cm²
③ Arc length — the angle stays 120°, the radius changes
3 cm: 6.28 cm6 cm: 12.6 cm9 cm: 18.8 cm12 cm: 25.1 cm
④ Same sector (radius 8 cm, angle 90°) — what changes is what you are asked to find
the arc length: 12.6 cmthe area: 50.3 cm²the perimeter: 28.6 cm
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