Concentric circles
Concentric circles are two or more circles sharing the same center point but having different radii. In Grade 6 Saxon Math Course 1, students recognize concentric circles in targets, ripples, and cross-sections of cylinders. The ring-shaped region between two concentric circles is called an annulus. If an inner circle has radius 3 cm and an outer circle has radius 7 cm, the annulus area is π(7²) − π(3²) = π(49 − 9) = 40π cm². Understanding concentric circles deepens spatial reasoning and circle geometry.
Key Concepts
Property Concentric circles are circles with the same center.
Examples The rings on an archery target are a classic example of concentric circles. Drawing a circle with a 3 cm radius and another with a 5 cm radius from the same center point creates concentric circles. The circular tracks on a running field, which curve around the same central green space, are parts of concentric circles.
Explanation Picture the rings on a bull's eye target or the ripples spreading out after a stone is tossed into a pond. Those are concentric circles! They all share the exact same center point but have different radii, creating a cool pattern of circles within circles. It’s like a whole family of circles living at the same address.
Common Questions
What are concentric circles?
Circles that share the same center point but have different radii — like a bullseye target.
What is the region between two concentric circles called?
An annulus — the ring-shaped area between the inner and outer circles.
How do you find the area of an annulus?
Subtract the inner circle's area from the outer circle's area: A = π R² − π r² = π(R² − r²).
Two concentric circles have radii 3 cm and 7 cm. What is the annulus area?
π(7² − 3²) = π(49 − 9) = 40π ≈ 125.7 cm².
Give two real-world examples of concentric circles.
A dartboard/bullseye target and ripples spreading outward from a pebble dropped in water.