Mathematics
Grade 6
15 min
Area between two circles
Area between two circles
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1
Introduction & Learning Objectives
Learning Objectives
Identify and describe concentric circles.
Understand that the area between two concentric circles is found by subtracting the area of the smaller circle from the area of the larger circle.
Calculate the area of a single circle given its radius (using an approximate value for pi).
Apply the concept of subtraction to find the area of the region between two concentric circles.
Solve real-world problems involving the area between two circles.
Accurately label units for area measurements.
Have you ever seen a target board or a donut? š© How much space is covered by the colored ring, not the whole circle?
In this lesson, we'll learn how to find the space, or area, between two circles that share the same center. This skill helps us understand how to measur...
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Key Concepts & Vocabulary
TermDefinitionExample
CircleA round shape where all points on the edge are the same distance from the center.A dinner plate is a circle.
RadiusThe distance from the center of a circle to any point on its edge.If you measure from the center of a pizza to its crust, that's the radius.
AreaThe amount of surface inside a two-dimensional shape, measured in square units.The area of a square floor tile might be 1 square foot.
Concentric CirclesTwo or more circles that share the exact same center point but have different radii.The rings of a target board are concentric circles.
Area of a CircleThe space covered by a single circle, calculated using its radius and a special number called pi (approximately 3.14).A circle with a radius of 2 cm has an area of about 3.14 x 2 x 2 = 12.56 square cm....
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Core Formulas
Area of a Circle Formula
A = \pi \times r \times r
Use this formula to find the total space covered by a single circle. 'A' stands for Area, '\pi' (pi) is a special number approximately 3.14, and 'r' is the radius of the circle.
Area Between Two Concentric Circles
A_{between} = A_{large} - A_{small}
To find the area of the region between two circles that share the same center, calculate the area of the larger circle and subtract the area of the smaller circle from it.
5 more steps in this tutorial
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Challenging
The area of the ring between two concentric circles is exactly equal to the area of the inner circle. What is the relationship between the area of the large circle and the area of the small circle?
A.The large circle's area is 1.5 times the small circle's area.
B.The large circle's area is double the small circle's area.
C.The large circle's area is triple the small circle's area.
D.The large circle's area is four times the small circle's area.
Challenging
The radius of a small circle is 5 cm. The radius of a larger concentric circle is 20% greater than the small circle's radius. What is the area of the ring between them? (Use Ļ ā 3.14)
A.34.54 cmĀ²
B.3.14 cmĀ²
C.15.7 cmĀ²
D.113.04 cmĀ²
Challenging
The radii of two concentric circles are in the ratio 2:3. The area of the smaller circle is 50.24 inĀ². What is the area of the ring between the circles? (Use Ļ ā 3.14)
A.25.12 inĀ²
B.113.04 inĀ²
C.75.36 inĀ²
D.62.80 inĀ²
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