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Area and Circumference of a Circle Worksheets

When we are working with circles, we often need to know two measures about them and those are area and circumference. These measures give us a good deal of insight into the nature of the circle. Circumference is just a fancy way of asking for the perimeter of this specific geometric shape. It is the distance around the edges. This is a very practical measure that is used in the real world often from determining how many times a tire will rotate on a car or weather a huge tree will fit on a tractor bed to be transported. You can see this measure displayed below, if you would like. Area is a measure of the region that encompasses all the stuff inside the circle itself. This has many practical uses as well. Just about any company that makes any product that is made with round molds like lens is constantly measuring this value to understand the cost of their product. These worksheets and lesson will help you learn the concept of these measures on this geometric shape and how to calculate them in a wide range of situations.

Aligned Standard: Grade 7 Geometry - 7.G.B.4

  • Answer Keys - These are for all the unlocked materials above.

Homework Sheets

You don't even want to hear how long it took me to think up things that were characteristically perfect circles.

  • Homework 1 - Ryan made a mini round bed for his friend.He wants to put a bed sheet. If the bed is 10 feet in diameter, how many square feet of bedding will he need to buy to cover the bed? Use 3.14 for pi
  • Homework 2 - Tia buys a CD. Then she calculated that it has a circumference of 120 cm. What is the CD's diameter? Use 3.14 for pi.
  • Homework 3 - Ryan bought 1kg of lemons. He didn't find a basket to keep them in. So he put in a round vessel. If the diameter of the vessel is 32, what is the area and circumference of the round vessel?

Practice Worksheets

I did give up a few times when writing these and just say that you are a circle.

  • Practice 1 - Sara measured the bowl. Then she calculated that it has a circumference of 70 cm. What is the bowl's diameter?
  • Practice 2 - You will find raw examples here as well as practical applications that you can work with.
  • Practice 3 - Roy made a tasty burger. The diameter of the burger was 22 cm. What was the area of the burger?

Math Skill Quizzes

These are verbatim what you could expect to see on any assessment for this standard.

  • Quiz 1 - Find the circumference of the circles.
  • Quiz 2 - Find the area of the circle if the radius is 11.
  • Quiz 3 - A quick assessment of both measures.

How to Determine the Area and Circumference of a Circle

A circle is a geometric shape that lacks any edges or corners which makes it pretty easy to spot. We have studied about the concept and have defined the anatomy of a circle in detail. There are eight common measures that we can examine in circles the most common being the measures of radius, diameter, and circumference. The radius is the distance from the center point to endpoint on the curve of the figure. The diameter can be defined mathematically as two times the radius, but it is a straight line that passes from an end point to another endpoint of the figure while passing directly through the center point. Circumference is a name used to describe the perimeter of a circle or distance around it. However, studying these parts is easier than solving the problems that include them within it. Do not worry, we are here to help you out in solving these problems. The common measures of this shape which become a very common geometric problem is how to determine the area and circumference of these so unique structures. You can see all these measured displayed in the image of the blue circle below:

Radius, Diameter, and Circumference Visual

Circumference and area are often confused as the same thing. The circumference is the enclosing boundary of the circle, while area is the space occupied by the circle. However, both share some common factors. Here we will examine these factors:

Radius - As we examined this before, this is a measure of the distance from the center of the figure to any point on its circumference. Calculating area or circumference requires us to know the radius of the circle.

Pi - Pi (ℼ) is defined as the ratio of circumference to the circle's diameter. Regardless of the size of a figure, this ratio will always equal this value. But don't worry, you don't need to calculate it. It is a constant value, and it won't take you more than twice to learn it by heart. The value of pi is 3.14.

Calculating Circumference - Circumference of a circle is denoted by the capital letter (C) and is states as twice its radius into the constant pi. To mathematically express it:

C= 2 (ℼ) r

Taking r = 4 inches and (ℼ) = 3.14

C = 2 (3.14) 4

C = 25.12 inches

Calculating Area - The area of a circle is equal to squared radius times constant pi (ℼ). You can find the area of these figures by using the following equation:

A = (ℼ)r2

If we had a circle with a radius of 3 inches and (ℼ) = 3.14, we would solve for the area of the circle in this way:

A = 3.14 (3)2, A = 3.14 x 9, A= 28.26 inches

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