Mathematics
Grade 6
15 min
Circles: word problems
Circles: word problems
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the key parts of a circle (radius, diameter, circumference) from a word problem.
Differentiate between radius and diameter and understand their relationship.
Recall and apply the formula for the circumference of a circle.
Use the approximation of Pi (π ≈ 3.14 or π ≈ 22/7) in calculations.
Translate real-world scenarios into mathematical problems involving circles.
Solve multi-step word problems involving the circumference of circles.
Clearly state the units in their final answers for circle word problems.
Have you ever wondered how much string you'd need to go around a hula hoop, or how far a bicycle wheel travels in one spin? 🚴♀️ Today, we'll learn how to solve these kinds of 'circle' mysteries!
In this lesson, you'...
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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 coin, a pizza, or a clock face are all examples of circles.
CenterThe exact middle point of a circle, from which all points on the edge are equally distant.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 pizza has a radius of 8 inches, its diameter is 16 inches (8 inches * 2).
Circumference (C)The total distance around the outside edge of a circle.I...
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Core Formulas
Relationship between Radius and Diameter
$$d = 2r$$
The diameter (d) of a circle is always twice its radius (r). This means if you know one, you can find the other.
Circumference using Diameter
$$C = \pi d$$
To find the circumference (C) of a circle, multiply Pi (π) by its diameter (d). Use π ≈ 3.14 or π ≈ 22/7 for calculations.
Circumference using Radius
$$C = 2\pi r$$
To find the circumference (C) of a circle, multiply 2 by Pi (π) and then by its radius (r). This is the same as πd, since d = 2r.
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Challenging
The circumference of a large circular fountain is 50% of the circumference of a nearby circular garden. If the garden has a diameter of 30 meters, what is the radius of the fountain? Use π ≈ 3.14.
A.15 meters
B.7.5 meters
C.10 meters
D.5 meters
Challenging
A dog is on a leash tied to a pole. The leash allows the dog to run along a path that is a perfect semicircle with a diameter of 10 meters. What is the length of this semicircular path? Use π ≈ 3.14.
A.31.4 meters
B.10 meters
C.15.7 meters
D.25.7 meters
Challenging
A circular flower bed has a diameter of 14 feet. You want to place a decorative border around it that costs $2.50 per foot. What will be the total cost of the border? Use π ≈ 22/7.
A.$110.00
B.$35.00
C.$87.50
D.$220.00
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