colt-logan
Uploaded by
14 SLIDES
279 VUES
140LIKES

Understanding Geometry: Shapes, Solids, Area, and Volume Formulas

DESCRIPTION

Dive into the fundamentals of geometry with a comprehensive exploration of shapes, solids, and formulas for calculating area and volume. This guide covers key concepts such as vertices, edges, faces, and definitions for various geometric figures, including prisms, cylinders, pyramids, and cones. Learn how to find areas of rectangles, circles, and the volume of 3D shapes using established formulas. Also included are practical examples and applications, showcasing proportions and relationships, like the comparison of heights through shadows. Ideal for students and enthusiasts!

1 / 14

Télécharger la présentation

Understanding Geometry: Shapes, Solids, Area, and Volume Formulas

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. SHAPED Rafael López

  2. VERTICES, EDGES, FACES

  3. CIRCLES AREA: A= r2 CIRCUMFRANCE= C= d or C= 2 r C DIAMETER RADIUS

  4. Congruency C F A E D B ABC DEF

  5. FGHJKL - MNPQRS NP/GH=RQ/ KJ 6/4=X/2 4x=12 4x=12 4x/4=12/4 F G S 4 cm Cross Multiply R M L H Xcm N Q 6 cm J P K 2 cm

  6. APPLICATIONS AND PROPORTION Mans height / poles height= Mans shadow/ poles shadow 6/x= 3/45 3x= 270 3x/ 3=270/ 3 X=90 X ft 6 ft 45 ft 3 ft

  7. CHANGING DIMENSIONS PERIMETER: 2 (L) + 2 (W) Rectangle A: 2( 2) +2(W)=12 Rectangle B: 2( 6)+ 2 ( W)= 18 A B 4 6 AREA: L x W Rectangle A: 4x2 = 8 Rectangle B: 6x3 = 18 2 Sides: 4/6 =2/3 3 perimeters: 12/ 18= 2/3 Areas: 8/18 = 4/6 = (2/3) 2

  8. Viewing solids from different perspectives Front view Topview Sideview

  9. prism B: ½ x BxH B: ½ (13) (14) B: 39in.2 V: B xH V: (39) (4) V: 156 in. 3 Volume= ( Area of one base) x (Height of the prism )

  10. FORMULAS FOR VOLUME Prism BB x H B: area of base H: Height of prism Cube S3 S: length of one side Pyramid B: area of base H: Height of pyramid 1/3 B x H Cylinder r : Radius H: Height r2h Cone 1/3r2h r : Radius H: Height

  11. Volume of Sphere V= 4/3 r3 V= 4/3 (3.14) (33) V= 113.04 3 cm

  12. Classifying Solids A prism is a solid formed by two congruent polygon bases connected by rectangular lateral faces. A prism is named with regard to the polygon bases A cylinder is a solid formed by two congruent circular bases A pyramid is a solid formed by one polygon base. The lateral faces are triangles that meet at a vertex. A pyramid is named with regard to the polygon base. A cone is a solid formed by one circular base with a vertex at the opposite end

  13. Volume practice B: ½ x BxH B: ½ (8) ( 30) B: ½ ( 240) B: 120 V= r2h V= 3. 14 x (10 2)x 23 V= 3.14 x 20 x 23 V= 3.14 x 460 V= 1444.4 V: B x H V: 120 x 30 V: 3600

More Related