1. Types of curves simple curves: A curve is simple if it does not cross itself.

2. Types of Curves closed curves: a closed curve is a curve with no endpoints and which completely encloses an area curveareacurvearea

3. Types of Curves convex curve: If a plane closed curve be such that a straight line can cut it in at most two points, it is called a convex curve. Convex Curves Not Convex Curves

4. Circles Area = π r 2 Circumference = 2 π r or or Circumference = π d

5. Circles Otis is drawing a circle with a 4 inch radius. He wants to double the radius. How will this affect the area of the circle?

6. Circles Su is selling 12 inch diameter pumpkin pies for $6.50. How should she adjust her price (if she wants to be fair) when she reduces her pies to a 10 inch diameter?

7. Circles Javier’s bicycle tire has a 12 inch radius. How far will he travel...... in one rotation of the tire?... in 10 rotations of the tire?

9. Volume  Cylinder vs. Cone  Cube vs. Square pyramid

10. Area of Circle  draw a square, and inscribe a circle in it, which means to draw the circle inside the square so that the circle just touches each side of the square.  We can find the area of this square by first finding the area of the four smaller squares—each with sides equal to r, the radius of the circle—and adding them together.   Notice that the sides of the square are twice as long as the radius of the circle. You could also find the area of the square by multiplying the side times the side, or 2r x 2r, which also equals 4r2.  You can see that the area of the circle must be less than the area of four of the squares. But how much less? We could make an educated guess and say that the area of the circle might be a little bit larger than three of the smaller squares.  The actual number we're looking for, which is between 3 and 4, is the special number called pi, represented by the Greek letter. Pi is approximately equal to 3.14.   The symbol you see here means "approximately equal to." Pi actually has an unending number of decimal points, but 3.14 is usually close enough for our calculation purposes. Pi is the ratio between the diameter and circumference of a circle.  The final formula for the area of a circle is shown here. 