Transcript circle
Geometry – Circles Circles are shapes made up of all points in a plane that are the same distance from a point called the center. Look at this example of a circle: center diameter – the distance across a circle through its center circumference - the distance around a circle radius – the distance from the center to any point on a circle What is the distance around the circle? How much space is inside the circle? The distance around the circle is called the circumference. The space is inside the circle is called the area. The circumference of every circle is approximately three times longer than its diameter! C This relationship ( ) is where π or pi comes d from. To find the circumference or area of a circle, you must use this relationship or the value pi. 22 Pi ≈ 3.14 or 7 You may use whichever form you wish. If your problem contains multiples of seven (7), it makes sense to use the fractional form of pi. You will always be given the circle’s diameter or the radius. Your answer will be a linear measurement. The radius is always ½ of the diameter. The diameter is always radius. diameter – the distance across a circle through its center two times the radius – the distance from the center to any point on a circle The circumference formulas are found on the key of the FCAT Reference Sheet. Choose the correct formula for circumference. Use this formula if you have diameter (d) Use this formula if you have radius (r) Write the circumference formula exactly as it appears on the FCAT Reference Sheet. Rewrite the circumference formula substituting the values that you know. Solve one step at a time rewriting after each step. C = Πd C = 3.14 × 12 A = 28.26 meters Write the circumference formula exactly as it appears on the FCAT Reference Sheet. Rewrite the circumference formula substituting the values that you know. Solve one step at a time rewriting after each step. C = 2Πr C = 2 × 3.14 × 12 A = 75.36 meters Follow the same set of steps as before! Write the circumference formula exactly as it appears on the FCAT Reference Sheet. Rewrite the circumference formula substituting the values that you know. Solve one step at a time rewriting after each step. Solve the following problem: Find the diameter of a basketball hoop with a circumference of 56.52 inches. Use 3.14 for Π. C 56.52 18 in. = Πd = 3.14 × d Divide by 3.14 on both sides to undo the multiplication! =d 1. One is on the left. 50 m 14 m 2. One is on the right. Note: Use 22 7 for Π. 1. C = Πd 22 2 4. C = × 1 1 22 2. C = × 14 7 5. C = 22 14 3. C = × 7 1 6. C = 44 meters Since you are finding two halves, you can find one whole instead! 44 1 50 m 14 m You will always be given the circle’s diameter, radius, or its circumference. You need to find the value of radius before you begin! ½ of the diameter or r = d ÷ 2. The radius is always The diameter is equal to circumference divided by pi or 3.14. Or d = C 3.14 Sometimes you are given radius. This means less work!! Select the correct area formula: Write the area formula exactly as it appears on the FCAT Reference Sheet. Rewrite the area formula substituting the values that you know. Solve one step at a time rewriting after each step. 2 12 mm A = Πr A = 3.14 × r × r A = 3.14 × 12 × 12 A = 3.14 × 144 A = 452.16 mm2 Write the area formula exactly as it appears on the FCAT Reference Sheet. Rewrite the area formula substituting the values that you know. Solve one step at a time rewriting after each step. A = Πr2 r=d÷2 A = 3.14 × r × r r=6÷2 A = 3.14 × 3 × 3 r=3 A = 3.14 × 9 A = 28.26 ft2 6 feet Write the area formula exactly as it appears on the FCAT Reference Sheet. Rewrite the area formula substituting the values that you know. Solve one step at a time rewriting after each step. Divide your answer by 2! Note: You could also use the formula or 4 inches Remember to multiply by ½ or divide by 2! Choose the formula that you feel the most comfortable using. You are finding the area of one half of a circle! You can use this same method to find the circumference of one half of a circle! Remember that the shapes have two dimensions. When you multiply one measurement by another measurement you end up with square units. For Example: •Square Feet •ft2 •Square Inches •Square Centimeters •in2 •cm2 Remember to use the FCAT Reference Sheet: