Perimeters and areas of plane figures (circles)

Practice 5 items →

π is a number. An arc and a sector are fractions of the circle, so their length and area scale by θ/360°. Students use circumference, area, arc length, and sector area, and compose them with triangles and rectangles.

Specification · for a parent or teacher

Part no.: circles-arcs-sectors
Course: Advanced Math 7 · Unit 12
Realm: Shapes
Difficulty: 3 of 4 — Grade 6–7 core. Multi-step, first symbolic work.
Qty: 5 items

Part no. is the node's id; the realm is the kind of math; qty is how many practice items it carries.

Students can

those four; composites of sectors, triangles, rectangles.

Ready when

a 90° sector of $r=6$ , both arc length and area, in terms of $\pi$ .

Formulas

Circumference

C = 2\pi r = \pi d

Circle area

A = \pi r^2

Arc length

s = \frac{\theta}{360^\circ} \cdot 2\pi r

Sector area

A = \frac{\theta}{360^\circ} \cdot \pi r^2

Watch for

area of a sector using $\frac{\theta}{360}2\pi r$ ; mixing diameter and radius.

Before · requires

Area of plane figuresarea-triangles-trapezoids · Math 6
Ratiosratios-grade6 · Math 6

After · used by

Volume and surface area of solidsvolume-surface-3d · Math 7

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