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: \(S_{xq}=2\pi rh\) Total Area: \(S_{tp}=2\pi rh+2\pi r^2\) b. Cylindrical volume The volume of the cylinder is given by the formula: \(V=Sh=\pi r^2h\) 1.2. Cone a. … [Read more...] about Math 9 Review chapter 4: Cylinder – Cone – Sphere

# Math Lecture 9

## 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. - The semicircle in the above rotation … [Read more...] about Math 9 Chapter 4 Lesson 3: Sphere Sphere Area and Sphere Volume

## 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 is a cone centered \(O\). - The edge \(AC\) sweeps over … [Read more...] about Math 9 Chapter 4 Cones – Truncated cones – Surrounding area and volume of cones, truncated cones

## 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 cylinder. - Cylindrical birth lines (eg \(EF\)) are … [Read more...] about Math 9 Chapter 4 Lesson 1: Cylindrical – Area and volume of the cylinder

## 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 angles α ( 0 < α < 180°), the arc inside the angle is … [Read more...] about Math 9 Review chapter 3: Angle with a circle

## Math 9 Chapter 3 Lesson 10: Area of a circle, a circular fan

Math 9 Chapter 3 Lesson 10: Area of a circle, a circular fan 1. Summary of theory 1.1. Formula for calculating the area of a circle The area of a circle with radius R is calculated by the formula: \(S=\pi R^2\) 1.2. Formula to calculate the area of a circular fan The area of a circular fan of radius R, arc n0 is calculated by the … [Read more...] about Math 9 Chapter 3 Lesson 10: Area of a circle, a circular fan

## Math 9 Chapter 3 Lesson 9: Length of circles, arcs

Math 9 Chapter 3 Lesson 9: Length of circles, arcs 1. Summary of theory 1.1. Formula for calculating the length of a circle The length \(C\) of a circle with radius \(R\) is calculated by the formula: \(C = 2\pi R\) If \(d\) is the diameter of the circle \((d=2R)\) then \(C = πd\) 1.2. Formula for calculating arc length On a circle of radius … [Read more...] about Math 9 Chapter 3 Lesson 9: Length of circles, arcs

## Math 9 Chapter 3 Lesson 8: The circumcircle and the incircle

Math 9 Chapter 3 Lesson 8: The circumcircle and the incircle 1. Summary of theory 1.1. Define - The circle that passes through all the vertices of a polygon is called the circumcircle of the polygon and this polygon is called the incircle. The circle tangent to all sides of a polygon is called the incircle of the polygon and the polygon is called the … [Read more...] about Math 9 Chapter 3 Lesson 8: The circumcircle and the incircle

## Math 9 Chapter 3 Lesson 7: Inscribed quadrilateral

Math 9 Chapter 3 Lesson 7: Inscribed quadrilateral 1. Summary of theory 1.1. Concept Define: A quadrilateral with four vertices lying on the same circle is called a cyclic quadrilateral (or inscribed quadrilateral). For example, the quadrilateral \(ABCD\) has four vertices \(A,B,C,D\) lying on the same circle, so \(ABCD\) is called an inscribed … [Read more...] about Math 9 Chapter 3 Lesson 7: Inscribed quadrilateral

## Math 9 Chapter 3 Lesson 6: The arc containing the angle

Math 9 Chapter 3 Lesson 6: The arc containing the angle 1. Summary of theory 1.1. How to solve locus problem To prove that the locus (set) of points M satisfying the property \(\tau\) is a certain shape \(H\), we have to prove two parts: Pros: Every point with property \(\tau\) is in the shape \(H\). Island part: Every point in the shape \(H\) has … [Read more...] about Math 9 Chapter 3 Lesson 6: The arc containing the angle