Mathematics
Grade 7
15 min
Circles: calculate area, circumference, radius, and diameter
Circles: calculate area, circumference, radius, and diameter
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1
Introduction & Learning Objectives
Learning Objectives
Identify and define the parts of a circle, including radius and diameter.
Explain the concept of Pi (π) and its role in circle calculations.
Calculate the circumference of a circle given its radius or diameter.
Calculate the area of a circle given its radius or diameter.
Determine the radius or diameter of a circle given its circumference or area.
Apply circle formulas to solve real-world problems involving circular objects.
Have you ever wondered how much frosting you need for a round cake 🎂, or how far a bicycle wheel travels in one spin? These questions all involve understanding circles!
In this lesson, we'll explore the fascinating world of circles. You'll learn how to measure different parts of a circle, like its 'aroundness' (c...
2
Key Concepts & Vocabulary
TermDefinitionExample
CircleA set of all points in a plane that are the same distance from a central point.A hula hoop, a coin, or the outline of a plate are all examples of circles.
CenterThe central point from which all points on the circle are equidistant.If you draw a circle with a compass, the point where the compass needle sits is the center.
Radius (r)The distance from the center of a circle to any point on its edge.If a pizza has a radius of 8 inches, it means the distance from the center to the crust is 8 inches.
Diameter (d)The distance across a circle passing through its center. It's twice the length of the radius.If a clock face has a diameter of 12 inches, it means the distance straight across it, through the middle, is 12 inches.
Circumference (C)The distance around the...
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Core Formulas
Radius and Diameter Relationship
$d = 2r$ or $r = \frac{d}{2}$
Use these formulas to find the diameter if you know the radius, or to find the radius if you know the diameter.
Circumference of a Circle
$C = \pi d$ or $C = 2\pi r$
Use these formulas to find the distance around a circle. Use $\pi d$ if you know the diameter, or $2\pi r$ if you know the radius. Remember to use an approximation for $\pi$ (like 3.14 or 22/7).
Area of a Circle
$A = \pi r^2$
Use this formula to find the amount of space inside a circle. Remember that $r^2$ means $r \times r$. If you are given the diameter, first find the radius by dividing the diameter by 2.
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Challenging
A square piece of cardboard has a side length of 20 cm. The largest possible circle is cut out from it. What is the area of the cardboard that is left over? Use π ≈ 3.14.
A.86 cm²
B.314 cm²
C.400 cm²
D.271.2 cm²
Challenging
A circular fountain has a radius of 5 meters. It is surrounded by a circular path that is 3 meters wide. What is the area of the path itself? Use π ≈ 3.14.
A.78.5 m²
B.200.96 m²
C.122.46 m²
D.28.26 m²
Challenging
If you double the radius of a circle, what happens to its area?
A.The area doubles.
B.The area is halved.
C.The area quadruples (becomes 4 times larger).
D.The area stays the same.
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