{"appState":{"pageLoadApiCallsStatus":true},"articleState":{"article":{"headers":{"creationTime":"2017-11-29T03:33:00+00:00","modifiedTime":"2017-11-29T03:33:00+00:00","timestamp":"2022-09-14T18:16:03+00:00"},"data":{"breadcrumbs":[{"name":"Academics & The Arts","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33662"},"slug":"academics-the-arts","categoryId":33662},{"name":"Study Skills & Test Prep","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33772"},"slug":"study-skills-test-prep","categoryId":33772},{"name":"GED","_links":{"self":"https://dummies-api.dummies.com/v2/categories/33783"},"slug":"ged","categoryId":33783}],"title":"GED Math Extra Prep: Circumference and Area of a Circle","strippedTitle":"ged math extra prep: circumference and area of a circle","slug":"ged-math-extra-prep-circumference-area-circle","canonicalUrl":"","seo":{"metaDescription":"The GED Math test will probably contain questions that ask you to work with the circumference and area formulas for a circle. As you'll see in the following pra","noIndex":0,"noFollow":0},"content":"The GED Math test will probably contain questions that ask you to work with the circumference and area formulas for a circle. As you'll see in the following practice questions, some of these problems will be a little more involved than simply plugging in numbers.\r\n<h2 id=\"tab1\" >Practice Questions</h2>\r\nA large circular pizza has an 18-inch diameter and is cut into 8 equal slices.\r\n\r\n<img class=\"alignnone size-full wp-image-247487\" src=\"https://www.dummies.com/wp-content/uploads/ged-pizza.jpg\" alt=\"ged-pizza\" width=\"400\" height=\"400\" />\r\n<ol>\r\n \t<li>What is the perimeter of one slice of the pizza?\r\n<img class=\"alignnone size-full wp-image-247488\" src=\"https://www.dummies.com/wp-content/uploads/eq0601.jpg\" alt=\"eq0601\" width=\"116\" height=\"81\" /></li>\r\n \t<li>What is the radius (in cm) of a circle whose circumference happens to equal its area (in cm<sup>2</sup>)?\r\n<strong>A.</strong> 2 cm\r\n<strong>B.</strong> 3 cm\r\n<strong>C.</strong> 5 cm\r\n<strong>D.</strong> 10 cm</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and Explanations</h2>\r\n<ol>\r\n \t<li>The correct answer is C.\r\n\r\nThe equation for the circumference of a circle is\r\n\r\n<img class=\"alignnone size-full wp-image-247489\" src=\"https://www.dummies.com/wp-content/uploads/eq0602.jpg\" alt=\"eq0602\" width=\"57\" height=\"20\" />\r\n\r\nSubstituting the value of the diameter into the equation gives you\r\n\r\n<img class=\"alignnone size-full wp-image-247490\" src=\"https://www.dummies.com/wp-content/uploads/eq0603.jpg\" alt=\"eq0603\" width=\"64\" height=\"20\" />\r\n\r\nThe perimeter of the slice is the distance around the edge of the slice, which equals two radii (2 times 9 inches) plus the length of the curved edge. There are eight pieces of pizza, so the length of the curved edge of the slice represents one-eighth of the entire circumference:\r\n\r\n<img class=\"alignnone size-full wp-image-247491\" src=\"https://www.dummies.com/wp-content/uploads/eq0604.jpg\" alt=\"eq0604\" width=\"211\" height=\"45\" />\r\n\r\nThe perimeter of the slice equals\r\n\r\n<img class=\"alignnone size-full wp-image-247492\" src=\"https://www.dummies.com/wp-content/uploads/eq0605.jpg\" alt=\"eq0605\" width=\"141\" height=\"21\" />\r\n\r\nso the correct answer is Choice (C).</li>\r\n \t<li>The correct answer is A.\r\n\r\nThe equation for the area of a circle is\r\n\r\n<img class=\"alignnone size-full wp-image-247493\" src=\"https://www.dummies.com/wp-content/uploads/eq0606.jpg\" alt=\"eq0606\" width=\"61\" height=\"25\" />\r\n\r\nand the equation for the circumference of a circle is\r\n\r\n<img class=\"alignnone size-full wp-image-247494\" src=\"https://www.dummies.com/wp-content/uploads/eq0607.jpg\" alt=\"eq0607\" width=\"63\" height=\"20\" />\r\n\r\nBecause the circumference of this particular circle happens to equal its area, you can set the equations equal to each other and solve for <em>r.</em> Dividing both sides of the equation by\r\n\r\n<img class=\"alignnone size-full wp-image-247495\" src=\"https://www.dummies.com/wp-content/uploads/eq0608.jpg\" alt=\"eq0608\" width=\"23\" height=\"17\" />\r\n\r\ngives you\r\n\r\n<img class=\"alignnone size-full wp-image-247496\" src=\"https://www.dummies.com/wp-content/uploads/eq0609.jpg\" alt=\"eq0609\" width=\"84\" height=\"112\" />\r\n\r\nTherefore, Choice (A) is the correct answer.</li>\r\n</ol>","description":"The GED Math test will probably contain questions that ask you to work with the circumference and area formulas for a circle. As you'll see in the following practice questions, some of these problems will be a little more involved than simply plugging in numbers.\r\n<h2 id=\"tab1\" >Practice Questions</h2>\r\nA large circular pizza has an 18-inch diameter and is cut into 8 equal slices.\r\n\r\n<img class=\"alignnone size-full wp-image-247487\" src=\"https://www.dummies.com/wp-content/uploads/ged-pizza.jpg\" alt=\"ged-pizza\" width=\"400\" height=\"400\" />\r\n<ol>\r\n \t<li>What is the perimeter of one slice of the pizza?\r\n<img class=\"alignnone size-full wp-image-247488\" src=\"https://www.dummies.com/wp-content/uploads/eq0601.jpg\" alt=\"eq0601\" width=\"116\" height=\"81\" /></li>\r\n \t<li>What is the radius (in cm) of a circle whose circumference happens to equal its area (in cm<sup>2</sup>)?\r\n<strong>A.</strong> 2 cm\r\n<strong>B.</strong> 3 cm\r\n<strong>C.</strong> 5 cm\r\n<strong>D.</strong> 10 cm</li>\r\n</ol>\r\n<h2 id=\"tab2\" >Answers and Explanations</h2>\r\n<ol>\r\n \t<li>The correct answer is C.\r\n\r\nThe equation for the circumference of a circle is\r\n\r\n<img class=\"alignnone size-full wp-image-247489\" src=\"https://www.dummies.com/wp-content/uploads/eq0602.jpg\" alt=\"eq0602\" width=\"57\" height=\"20\" />\r\n\r\nSubstituting the value of the diameter into the equation gives you\r\n\r\n<img class=\"alignnone size-full wp-image-247490\" src=\"https://www.dummies.com/wp-content/uploads/eq0603.jpg\" alt=\"eq0603\" width=\"64\" height=\"20\" />\r\n\r\nThe perimeter of the slice is the distance around the edge of the slice, which equals two radii (2 times 9 inches) plus the length of the curved edge. There are eight pieces of pizza, so the length of the curved edge of the slice represents one-eighth of the entire circumference:\r\n\r\n<img class=\"alignnone size-full wp-image-247491\" src=\"https://www.dummies.com/wp-content/uploads/eq0604.jpg\" alt=\"eq0604\" width=\"211\" height=\"45\" />\r\n\r\nThe perimeter of the slice equals\r\n\r\n<img class=\"alignnone size-full wp-image-247492\" src=\"https://www.dummies.com/wp-content/uploads/eq0605.jpg\" alt=\"eq0605\" width=\"141\" height=\"21\" />\r\n\r\nso the correct answer is Choice (C).</li>\r\n \t<li>The correct answer is A.\r\n\r\nThe equation for the area of a circle is\r\n\r\n<img class=\"alignnone size-full wp-image-247493\" src=\"https://www.dummies.com/wp-content/uploads/eq0606.jpg\" alt=\"eq0606\" width=\"61\" height=\"25\" />\r\n\r\nand the equation for the circumference of a circle is\r\n\r\n<img class=\"alignnone size-full wp-image-247494\" src=\"https://www.dummies.com/wp-content/uploads/eq0607.jpg\" alt=\"eq0607\" width=\"63\" height=\"20\" />\r\n\r\nBecause the circumference of this particular circle happens to equal its area, you can set the equations equal to each other and solve for <em>r.</em> Dividing both sides of the equation by\r\n\r\n<img class=\"alignnone size-full wp-image-247495\" src=\"https://www.dummies.com/wp-content/uploads/eq0608.jpg\" alt=\"eq0608\" width=\"23\" height=\"17\" />\r\n\r\ngives you\r\n\r\n<img class=\"alignnone size-full wp-image-247496\" src=\"https://www.dummies.com/wp-content/uploads/eq0609.jpg\" alt=\"eq0609\" width=\"84\" height=\"112\" />\r\n\r\nTherefore, Choice (A) is the correct answer.</li>\r\n</ol>","blurb":"","authors":[{"authorId":8947,"name":"The Experts at Dummies","slug":"the-experts-at-dummies","description":"The Experts at Dummies are smart, friendly people who make learning easy by taking a not-so-serious approach to serious 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GED Math Extra Prep: Circumference and Area of a Circle

By: The Experts at Dummies and

Updated: 11-29-2017

From The Book: GED Test

GED Test

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The GED Math test will probably contain questions that ask you to work with the circumference and area formulas for a circle. As you'll see in the following practice questions, some of these problems will be a little more involved than simply plugging in numbers.

Practice Questions

A large circular pizza has an 18-inch diameter and is cut into 8 equal slices.

ged-pizza

What is the perimeter of one slice of the pizza?
What is the radius (in cm) of a circle whose circumference happens to equal its area (in cm²)? A. 2 cm B. 3 cm C. 5 cm D. 10 cm

Answers and Explanations

The correct answer is C.
The equation for the circumference of a circle is
Substituting the value of the diameter into the equation gives you
The perimeter of the slice is the distance around the edge of the slice, which equals two radii (2 times 9 inches) plus the length of the curved edge. There are eight pieces of pizza, so the length of the curved edge of the slice represents one-eighth of the entire circumference:
The perimeter of the slice equals
so the correct answer is Choice (C).
The correct answer is A.
The equation for the area of a circle is
and the equation for the circumference of a circle is
Because the circumference of this particular circle happens to equal its area, you can set the equations equal to each other and solve for r. Dividing both sides of the equation by
gives you
Therefore, Choice (A) is the correct answer.

About This Article

This article is from the book:

GED Test ,

About the book author:

Stuart Donnelly, PhD, earned his doctorate in mathe-matics from Oxford University at the age of 25. Since then, he has established successful tutoring services in both Hong Kong and the United States and is considered by leading educators to be one of the most experienced and qualified private tutors in the country.

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GED ,