S OLVING FOR R ADIUS AND D IAMETER

W HAT IF WE WANTED TO FIND THE RADIUS AND DIAMETER OF A CIRCLE GIVEN THE AREA ? Use π = 3.14 to find the radius of this circle. A = πr² A = 100 cm How can we rearrange this to make the radius the subject of the formula? ? r² = A π How can we undo r² ? We need to learn how to take the square root of a number.

Think about the relationship between the area of a square and the length of one of its sides. Taking the square root of a number is the inverse operation of squaring the number. 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. area = 36 square units side length = 6 2 = 36 R ELATIONSHIPS AND D EFINITIONS 6 units 36 = 6

P ERFECT S QUARES These are perfect squares. They have the same length and the same width. Area = length ∙ width

What are the square roots of 81? 9 2 = 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? F INDING S QUARE R OOTS ± 7

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. W HEN YOU DON ’ T HAVE PERFECT SQUARES …

What are the square roots of 78? What are the square roots of 173? Y OU T RY ! 8.83 and (±8.83) and (±13.15)

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? Using Square Roots to Solve for Radius No. Because a radius is a distance. Distance is always measured in positive numbers. r

W HAT IF WE WANTED TO FIND THE RADIUS AND DIAMETER OF A CIRCLE GIVEN THE AREA ? Use π = 3.14 to find the radius of this circle. A = πr² A = 100 cm How can we rearrange this to make the radius the subject of the formula? ? r² = A π r = r = 5.64 cm Always round your answer to the nearest hundredth. We can also find the diameter since d = 2r d = cm

A TABLECLOTH FOR A ROUND TABLE HAS AN AREA OF 1,386 IN ². W HAT IS THE APPROXIMATE RADIUS OF THE TABLECLOTH ? Area = πr 2 1,386 = (3.14)r 2 r = in Example r =

F IND THE R ADIUS Find the diameter of a circle that has an area of square yards. Use 3.14 for.

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