Amy has a master's degree in secondary education and has taught math at a public charter high school.
Watch this video lesson to learn how you can solve word problems that involve circles. Learn how the properties of circles make your problem-solving life that much easier and quicker.
In this lesson, we talk about circles and how they can help us solve problems. A circle is a 2-dimensional shape where the border is always the same distance from a fixed center point. Circles can be found all around us. Many clock faces are circles, as are watches. Wheels and tires are also circles. If we were to take a trip into outer space, we would look back and see that our planet earth is also a circle. A lot of our foods are also circles. My favorite is the pizza - the pepperoni pizza! Can you think of other things that are also circles?
A Word Problem
Because so many things around us are circular in shape, we can use their properties to help us solve problems. This problem, for example, can be easily solved by using circles.
A bicycle shop needs to replace the tubing inside a bicycle wheel. How long does the tubing need to be if the diameter of the wheel is 26 inches?
Do you notice the circle in this problem? Yes, the wheel of the bicycle is a circle. What is the problem asking us to find? The problem is asking us how much tubing is needed. Well, where does the tubing go? It goes all around the edge of the wheel. Isn't this the circumference of our circle? That's right! So, we will use the circumference property of circles to help us solve the problem. We remember that the formula to find the circumference is C = 2 * pi * r, where r is the radius and pi is approximately 3.14. Let's see now how we use this formula in our problem.
The formula C = 2 * pi * r uses the radius of a circle. But our problem only gives us the diameter. What can we do? We remember that our diameter is two times the radius, so we can actually just divide our diameter by 2 to find our radius. So, dividing the 26 by 2 gives us 26 / 2 = 13. So, our radius is 13. Now we can plug this 13 into the formula C = 2 * pi * r for C. Plugging it in and evaluating, we get C = 2 * 3.14 * 13 = 81.64 inches. So, the tubing needs to be 81.64 inches long for it to fit in the wheel.
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Sue the baker is finishing up a cake she is making for a special anniversary party. She needs to figure out how much whipping cream she needs to cover the top of her cake. The cake has a radius of 6 inches. What is the area on top that Sue needs to cover with her whipping cream?
What shape do we have here? We have a cake in the shape of a circle. This circle has a radius of 6 inches. What is the problem asking us to find? It is asking us to find the area of this circle. We remember that the formula for area is A = pi * r^2. Since we know the radius, we can plug it into our formula directly and evaluate to find our answer. We get A = pi * 6^2 = 3.14 * 36 = 113.04 square inches. So, Sue needs 113.04 square inches of whipping cream to cover the top of her cake completely.
Let's review what we've learned now. A circle is a 2-dimensional shape where the border is always the same distance from a fixed center point. Because so many things around us are circular in shape, we can use their properties to help us solve problems.
With the lessons learned through this video, you could have amassed the knowledge required to:
Recite the formal definition of a circle
Illustrate some of the math equations used to measure circles
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