SME
Grade 7 Math · Geometry
Circumference and area of circles
Use this for “A circle has a radius of 3 cm. Find its circumference and its area.”
Diagram
Radius
Unrolled
Wedges
This is an example. Type your own values to start a new problem.
r
Radius
example
d
Diameter
calculated
C
Circumference
calculated
A
Area
calculated
n
Wedges
example
Formulas
d
=
2
×
r
(diameter
=
2
×
radius)
6 = 2 × 3
C
=
π
×
d
(circumference
=
π
×
diameter)
6π = π × 6
A
=
π
×
r
2
(area
=
π
×
radius²)
9π
=
π
×
3
2
Assumptions
•
Every point on the circle is the same distance, the radius, from the center.
•
π is the circumference divided by the diameter of any circle: about 3.14.
•
Cut into wedges and laid top and bottom, a circle is close to a parallelogram half the circumference long and a radius tall.
•
Area is in square units.
Step-by-step
WE KNOW
r = 3 cm (radius), n = 8 (wedges)
FIND
diameter (d), circumference (C), area (A)
Step 1 · Find diameter (d)
Use d = 2 × r (diameter = 2 × radius)
A diameter is two radii end to end through the center.
d
=
2
×
3
d
=
6
cm
Step 2 · Find circumference (C)
Use C = π × d (circumference = π × diameter)
Circumference is π times the diameter.
C
=
π
×
6
C
=
6π
cm
(≈
18.85
cm)
Step 3 · Find area (A)
Use A = π × r² (area = π × radius²)
Square the radius, then multiply by π.
A
=
π
×
3
2
A
=
9
×
π
A
=
9π
cm²
(≈
28.27
cm²)
Check
Put the numbers back in. Both sides should match.
6 = 2 × 3 ✓
6π = π × 6 ✓
9π
=
π
×
3
2
✓
Topic check
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