Circles and circumference (compass) Good Afternoon! Today we will be learning about Circles and circumference (compass) Let’s warm up : The radii of circles are given. Find is the circumference? 1) 4.8 cm 2) 16 ft 1) 30.14 cm 2) 100.5 ft The diameter of circle are given. Find is the circumference? 3) 31 cm 4) 15.75 ft 3) 97.34cm 4) 49.5 ft CONFIDENTIAL

Circles and circumference (compass) . Let’s review what we did in the last session We learnt about Circles and circumference (compass) . Circle: A circle is a shape with all points that are same distance from the center. O Radius The circle is named circle O since the center is at point O. Radius: The radius is a line segment that begins from the centre and touches any point on the circle. CONFIDENTIAL

The Diameter is equal to twice the radius. Review Diameter: The distance across a circle through the center is called the diameter. The Diameter is equal to twice the radius. Diameter = 2 × Radius O Diameter Circumference: The distance around a circle is called the circumference. The circumference of a circle is also called the perimeter of the circle. CONFIDENTIAL

Review Lines in a Circle The name of a line in a circle depends on its position in the circle. secant chord tangent A secant is a line that passes through any two points on a circle. A chord is a line that joins two points on the circumference of a circle. A tangent is a line that touches the circle at only one point. CONFIDENTIAL

Parts of a Circle An arc is a part of the circumference. Review Parts of a Circle An arc is a part of the circumference. Here, AB is the arc. A B arc AB O sector AOB A sector is the part of a circle between two radii. Here, AOB is the sector . CONFIDENTIAL

Review Parts of a Circle A segment is the part of a circle that is between a chord and the circumference. segment semicircle A semicircle is a half of a circle. CONFIDENTIAL

Review Circumference The Circumference is the distance around the edge of the circle. It is exactly Pi (the symbol is π) times the Diameter, so: Circumference = π × Diameter Since the Diameter is equal to twice the radius. So this is also true: Circumference = 2 × π × Radius CONFIDENTIAL

The radius of a circle is 2 inches. What is the diameter? Review The radius of a circle is 2 inches. What is the diameter? The radius of a circle = 2 inches Since the Diameter is equal to twice the radius. i.e. Diameter = 2 × Radius Diameter = 2 × Radius = 2 x 2 inches = 4 inches Replace radius with 2. The diameter of a circle = 4 inches CONFIDENTIAL

The radius of a circle is 2 inches. What is the circumference? Review The radius of a circle is 2 inches. What is the circumference? The radius of a circle = 2 inches We know that, Circumference = 2 × π × Radius Circumference = 2 x π x 2 = 2 x 3.14 x 2 = 12.56 Replace radius with 2. Replace π with 3.14. The circumference of a circle = 12.56 inches CONFIDENTIAL

The diameter of a circle is 5 meters. What is the circumference? Review The diameter of a circle is 5 meters. What is the circumference? The diameter of a circle = 5 meters We know that, Circumference = π × Diameter Circumference = π x 5 = 3.14 x 5 = 15.7 Replace diameter with 5. Replace π with 3.14. The circumference of a circle = 15.7 meters CONFIDENTIAL

2D vs. 3D (Solid Figures) & volume Let’s start with 2D vs. 3D (Solid Figures) & volume A 2-dimentional figure is a shape with length and width. It can be open or closed. Closed figures: These are those figures that start and end at the same point. The figures shown above are closed figures. CONFIDENTIAL

The figures shown above are Open figures. Open figures: These are those figures that do not start and end at the same point. The figures shown above are Open figures. CONFIDENTIAL

A circle is a closed figure, but it does not have straight sides. A polygon is a closed 2-dimentional figures with straight sides. They are made of straight lines, and the shape is "closed“. Polygon (straight sides) Not a Polygon (has a curve) Not a Polygon (open, not closed) A circle is a closed figure, but it does not have straight sides. A circle is not a polygon. A polygon can be grouped by the number of sides they have. CONFIDENTIAL

Names of Polygons Name Sides Shape Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 CONFIDENTIAL

A 3-dimentional figure: is a figure with length, width and height. 3-dimensional figure A 3-dimentional figure: is a figure with length, width and height. You can describe a 3- dimensional figure by its parts. vertex A face is a flat side. A base is a face on which the figure sits. An edge is where two faces meet. A vertex is where 3 or more faces meet. edge face base CONFIDENTIAL

Examples of 3-dimensional figure. Cube Cylinder A cube has 6 faces, 12 edges, 8 vertices 2 circular bases CONFIDENTIAL

Rectangular prism Triangular pyramid Rectangular prism Triangular pyramid has 4 faces, 6 edges, 4 vertices Rectangular prism has 4 faces, 12 edges, 8 vertices CONFIDENTIAL

Net for a square pyramid. Make a Net You can make a net for any solid figure. Net for a square pyramid. Cube Triangular Prism CONFIDENTIAL

Volume of a Cuboids Cuboids are a 3-dimensional shape. It has 3 different measurements. Height Width Depth The volume of he cube is found using the formula Volume = Height × Width × Depth CONFIDENTIAL

The dimensions of a Rectangular prism is given. Find its volume. Height = 6 cm Width = 4 cm Depth = 7 cm We know that the volume of he cube is found using the formula Volume = Height × Width × Depth = 6 × 4 × 7 = 168 The volume of a Rectangular prism = 168 cubic centimeter or cm3. CONFIDENTIAL

BREAK CONFIDENTIAL

Click on the link below for some exciting puzzle GAME Click on the link below for some exciting puzzle http://www.thekidzpage.com/onlinejigsawpuzzles/kids-jigsaw-puzzles/12-piece-jigsaw/03-27-07-littlebrother.html CONFIDENTIAL

Assignments Identify 3-dimentional figure. Tell how many faces, edges and vertices it has 1) 2) 1) 4 faces, 6 edges, 4 vertices 2) 6 faces, 12 edges, 8 vertices 3) 4) 3) 1 circular base 4) no face, edge or vertices CONFIDENTIAL

The dimensions of Rectangular prisms are given. Find their volume. 5) Height = 5 cm Width = 4 cm Depth = 6 cm 6) Height = 6 cm Width = 8 cm Depth = 11 cm 5) 120 cm3. 6) 528 cm3. 7) Height = 12 cm Width = 14 cm Depth = 7 cm 8) Height = 9 cm Width = 5 cm Depth = 8 cm 7) 1176 cm3. 8) 360 cm3. CONFIDENTIAL

A 2-dimentional figure is a shape with length and width. Very Good! Let's Review A 2-dimentional figure is a shape with length and width. It can be open or closed. Closed figures: These are those figures that start and end at the same point. The figures shown above are closed figures. CONFIDENTIAL

The figures shown above are Open figures. Review Open figures: These are those figures that do not start and end at the same point. The figures shown above are Open figures. A polygon is a closed 2-dimentional figures with straight sides. They are made of straight lines, and the shape is "closed“. A circle is a closed figure, but it does not have straight sides. A circle is not a polygon. CONFIDENTIAL

A polygon can be grouped by the number of sides they have. Review A polygon can be grouped by the number of sides they have. Name Sides Shape Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 CONFIDENTIAL

A 3-dimentional figure: is a figure with length, width and height. Review 3-dimensional figure A 3-dimentional figure: is a figure with length, width and height. You can describe a 3- dimensional figure by its parts. vertex A face is a flat side. A base is a face on which the figure sits. An edge is where two faces meet. A vertex is where 3 or more faces meet. edge face base CONFIDENTIAL

Examples of 3-dimensional figure. Review Examples of 3-dimensional figure. Cube Cylinder A cube has 6 faces, 12 edges, 8 vertices 2 circular bases Rectangular pyramid Triangular pyramid Triangular pyramid has 4 faces, 6 edges, 4 vertices Triangular pyramid has 4 faces, 12 edges, 8 vertices CONFIDENTIAL

Net for a square pyramid. Review Make a Net You can make a net for any solid figure. Net for a square pyramid. Cube Triangular Prism CONFIDENTIAL

Volume of a Cuboids Cuboids are a 3-dimensional shape. Review Volume of a Cuboids Cuboids are a 3-dimensional shape. It has 3 different measurements. Height Width Depth The volume of he cube is found using the formula Volume = Height × Width × Depth CONFIDENTIAL

The dimensions of a Rectangular prism is given. Find its volume. Review The dimensions of a Rectangular prism is given. Find its volume. Height = 6 cm Width = 4 cm Depth = 7 cm We know that the volume of he cube is found using the formula Volume = Height × Width × Depth = 6 × 4 × 7 = 168 The volume of a Rectangular prism = 168 cm2. CONFIDENTIAL

See you in the next session. You have done a nice job. See you in the next session. CONFIDENTIAL