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Solving for Radius and Diameter

Solving for Radius and Diameter. What if we wanted to find the radius and diameter of a circle given the area?. A. π. Use π = 3.14 to find the radius of this circle. A = π r². How can we rearrange this to make the radius the subject of the formula?. A = 100 cm. r² =. ?.

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Solving for Radius and Diameter

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  1. Solving for Radius and Diameter

  2. What if we wanted to find the radius and diameter of a circle given the area? A π Use π = 3.14 to find the radius of this circle. A= πr² How can we rearrange this to make the radiusthe subject of the formula? A = 100 cm r²= ? How can we undo r² ? We need to learn how to take the square root of a number.

  3. Relationships and Definitions Think about the relationship between the area of a square and the length of one of its sides. area = 36 square units side length = 6 units Taking the square root of a number is the inverse operation of squaring the number. 62 = 36 = 6 36 • Every positive number has two square roots, one positive and one negative. • One square root of 36 is 6, since 6 • 6 = 36. • The other square root of 36 is –6, since (–6) • (–6) is also 36. • You can write the square root of 36 as ±6, meaning “plus or minus” 6.

  4. Perfect Squares These are perfect squares. They have the same length and the same width. Area = length ∙ width

  5. Finding Square Roots • What are the square roots of 81? • 92 = 81 and (-9)2 = 81. • The square roots of 81 are 9 and -9. • We can write it as ± 9. • What are the square roots of 49? ± 7

  6. When you don’t have perfect squares… • Sometimes, when you find the square roots of a number, the square roots will NOT be WHOLE NUMBERS. • This is why you NEED your calculator. • Use the square root button to find the square roots. If you get a decimal number, round to the nearest hundredth.

  7. You Try! • What are the square roots of 78? • What are the square roots of 173? 8.83 and -8.83 (±8.83) 13.15 and -13.15 (±13.15)

  8. Using Square Roots to Solve for Radius When we are finding the square root of r² we are looking for the radius. We learned that taking the square root of a positive number gives us two square roots. One negative and one positive. Can a radius of a circle be negative? No. Because a radius is a distance. Distance is always measured in positive numbers. r

  9. What if we wanted to find the radius and diameter of a circle given the area? A π Use π = 3.14 to find the radius of this circle. A= πr² How can we rearrange this to make the radiusthe subject of the formula? A = 100 cm r²= ? r = r = 5.64 cm We can also find the diameter since d = 2r Always round your answer to the nearest hundredth. d = 11.28 cm

  10. Example A tablecloth for a round table has an area of 1,386 in². What is the approximate radius of the tablecloth? Area = πr2 1,386 = (3.14)r2 r = r = 21.01 in

  11. Find the Radius • Find the diameter of a circle that has an area of 615.44 square yards. Use 3.14 for .

  12. Practice Worksheet

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