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Comprehensive Area and Volume Calculations for Architectural 3D Modeling in AutoCAD

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This document provides in-depth calculations for various geometric shapes used in architectural modeling, focusing on a project that involves multiple floors. It includes detailed area computations for flat surfaces, rectangles, curved surfaces, and hemispheres derived from 2D and 3D models. The calculations illustrate the use of AutoCAD design principles for accurate floor outlines and conclude with a summary of the total area and volume for each section. Essential for engineers and architects, this guide serves as a valuable resource for effective design and analysis.

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Comprehensive Area and Volume Calculations for Architectural 3D Modeling in AutoCAD

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  1. Client

  2. Driving Questions • Calculations? • Geometrical Shapes?

  3. Floor Outlines

  4. AutoCad Design 3D Model 2D model

  5. Area of Each Floor Bottom Floor Flat Surface A= πr2 A= (3.14)(36)2 A=(3.14)1296 A= 4069.44 Area Flat Surface=4069.44 Curved surface A=½ 4π r2 A= ½ (4)(3.14)(362) A= 12.56(1296) A=½(16277.76) Area of Curved surface= 8138.88 72m 36 A= 4069.44m2 72m Area of hemisphere=AR + A F.S= 2592+ 4069.44=6661.44 Area of hemisphere=6661.44 Area of rectangle A= ½ B(H) A=½ 72(72) A=36(72) A=2592 Area of rectangle=2592 Total Area =Area r-Area h Total Area =2592-6661.44= 4069.44 Total Area =4069.44

  6. Area of Upper Floor Flat surface A= ½ 4π r2 A=½ x 4(3.14)18.00492 A=½ (4)3.14(324.1764) A=½ (12.56)(1017.91) A=2(4071.66) A=2035.8279 Curved Surface A= πr2 A=3.14(18.00492) A=3.14(324.1764) A=1017.91 18.0049 32.4346 A= 2035.83 64.4692 A=(½)Bh A=½(64.4692)(32.4346) A=32.2346(32.4346) A= 1045.52 Area of hemisphere=AR + A F.S= Area of hemisphere= 1045.52+2035.8279= 3081.3479 Total Area =Arear - Areah Total Area= 1045.52-3081.349= 2035.8279

  7. Area of Top Floor 4.50m 7.20m Area of a rectangle Area = b x h A = 21.62 x 10.81 A = 233.71m2 Area of a triangle Area = ½ b x h A = ½ (3.61)(2.69) A = (1.805)(2.69) A = 8.764m2 Area of a rectangle - Area of a triangle = Total Area 233.71 - 8.764 = 224.946m2 10.81m 21.62m

  8. Total Area

  9. Table of Areas

  10. Table of Volume

  11. Table of Construction Cost

  12. Table of Air Conditioned Space

  13. Engraved 3D Model

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