Math Lecture 9

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Math 9 Chapter 4 Lesson 1: Cylindrical – Area and volume of the cylinder

Math 9 Chapter 4 Lesson 1: Cylindrical – Area and volume of the cylinder 1. Summary of theory 1.1. Cylinder When we rotate the rectangle (ABCD) around a fixed side (CD), we get a cylinder. – The two bases are congruent circles and lie on two parallel planes. – (DC) is the axis of the …

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Math 9 Chapter 4 Cones – Truncated cones – Surrounding area and volume of cones, truncated cones

Math 9 Chapter 4 Cones – Truncated cones – Surrounding area and volume of cones, truncated cones 1. Summary of theory 1.1. Cone When a right angled triangle (AOC) is rotated around the side of a fixed right angle (OA), a cone is obtained. – The side (OC) forms the base of the cone, which …

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Math 9 Chapter 4 Lesson 3: Sphere Sphere Area and Sphere Volume

Math 9 Chapter 4 Lesson 3: Sphere Sphere Area and Sphere Volume 1. Summary of theory 1.1. Globular When rotating a semicircle with center (O), radius (R) one circle around a fixed diameter (AB), a sphere is obtained. – The point (O) is called the center, the length (R) is the radius of the sphere. …

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Math 9 Review chapter 4: Cylinder – Cone – Sphere

Math 9 Review chapter 4: Cylinder – Cone – Sphere 1. Summary of theory 1.1. Cylinder a. Area around the cylinder With base radius r and height h, we have: Surrounding area: (S_{xq}=2pi rh) Total Area: (S_{tp}=2pi rh+2pi r^2) b. Cylindrical volume The volume of the cylinder is given by the formula: (V=Sh=pi r^2h) 1.2. …

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Math 9 Review chapter 3: Angle with a circle

Math 9 Review chapter 3: Angle with a circle 1. Summary of theory 1.1. Angle in the center An angle whose vertex coincides with the center of the circle is called a central angle. The two sides of the central angle intersect the circle at two points, thus dividing the circle into two arcs. For …

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Math 9 Chapter 3 Lesson 1: The central angle and the measure of the arc

Math 9 Chapter 3 Lesson 1: The central angle and the measure of the arc 1. Summary of theory 1.1. Angle in the center An angle whose vertex coincides with the center of the circle is called a central angle. The two sides of the central angle intersect the circle at two points, thus dividing …

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Math 9 Chapter 3 Lesson 2: The relationship between bow and string

Math 9 Chapter 3 Lesson 2: The relationship between bow and string 1. Summary of theory 1.1. Theorem 1 For two minor arcs in the same circle or two equal circles: a) Two equal arcs stretch two equal strings b) Two equal strings stretch two equal arcs – (stackrelfrown{AB}=stackrelfrown{CD}Rightarrow AB=CD) – (AB=CDRightarrowstackrelfrown{AB}=stackrelfrown{CD}) 1.2. Theorem 2 …

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Math 9 Chapter 3 Lesson 3: Inscribed angle

Math 9 Chapter 3 Lesson 3: Inscribed angle 1. Summary of theory 1.1. Define An inscribed angle is an angle whose vertex lies on a circle and whose sides contain two chords of that circle. The arc inside the angle is called the intercepted arc. The angle (widehat{BAC}) is called the inscribed angle, the intercepted …

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