University of Santo Tomas Module 1 Handouts PDF

05/07/2023 1 Prayer 2 2 1  05/07/2023 ------------------------- Introduction and Review of Relevant Topics and Basic Geometry ARC 116: SOLID MENSURATI...

05/07/2023 1 Prayer 2 2 1  05/07/2023 ------------------------- Introduction and Review of Relevant Topics and Basic Geometry ARC 116: SOLID MENSURATION – MODULE 1 ------------------------- 3 ------------------- Objectives ------------------- Discuss solid mensuration and its significance in architecture. Implement the correct way of showing computations. Review relevant topics in Mathematics that are useful in this course. 4 4 2  05/07/2023 --------------------- Outline --------------------- Solid Mensuration Computation Suggestions Review of Relevant Topics: Basic Math Equations Conversion of Units Basic Geometry 5 5 ▪ Topic dealing with the use of What is Solid formulae to calculate Perimeters, Mensuration? Areas, and Volumes of plane figures and solid forms. 6 6 3  05/07/2023 ▪ Various formulae are used extensively in structural design and construction (road, bridge, Why is it buildings, utilities) and in a large variety of architectural and necessary to engineering projects. study Solid Mensuration? ▪ Concepts in geometry can also be used in ________________ quantity surveys and ________________________ material/cost estimation for design and construction projects. 7 Scope PLANE FIGURES ▪ Shapes that only has two dimensions (e.g. width and height) and NO thickness. ▪ Area, Perimeter 8 4  05/07/2023 Scope SOLID FORMS ▪ Geometric figures in three dimensions. ▪ Has height, width and depth. ▪ Surface Area, Volume 9 10 10 5  05/07/2023 1. Draw an appropriate figure on which all dimensions are shown. 2. Write down all the formulae where unknown quantities are to be found. 3. It is helpful to use consistent and logical variables to denote numerical values in the solution. 4. Familiarize yourself with your scientific calculator. COMPUTATION SUGGESTIONS 11 Review of Relevant Topics Basic Math Equations Conversion of Units Basic Geometry 12 12 6  05/07/2023 BASIC MATH EQUATIONS RELEVANT TO THIS COURSE Pythagorean Theorem Distance Formula SOH-CAH-TOA Sine Law Cosine Law 13 13 BASIC MATH EQUATIONS RELEVANT TO THIS COURSE Solving for the length of a side of a right Pythagorean Theorem triangle, given the other two sides. Distance Formula hypotenuse SOH-CAH-TOA Sine Law Cosine Law 14 14 7  05/07/2023 BASIC MATH EQUATIONS RELEVANT TO THIS COURSE Solving for the distance between two points, Pythagorean Theorem given the X and Y coordinates of both points. Distance Formula SOH-CAH-TOA Sine Law Cosine Law 15 15 BASIC MATH EQUATIONS RELEVANT TO THIS COURSE Pythagorean Theorem Relates the sides to the corresponding opposite angles Distance Formula inside the right triangle to solve for SOH-CAH-TOA any unknown length or angle. Sine Law Cosine Law 16 16 8  05/07/2023 BASIC MATH EQUATIONS RELEVANT TO THIS COURSE Pythagorean Theorem Applicable for any triangle. It relates the Distance Formula length of the sides and the sine of the SOH-CAH-TOA corresponding (opposite) Sine Law angles inside the figure. Cosine Law 17 17 BASIC MATH EQUATIONS RELEVANT TO THIS COURSE Pythagorean Theorem Applicable for any triangle. It relates the Distance Formula length of the sides and the cosine of the SOH-CAH-TOA corresponding (opposite) Sine Law angle inside the figure. Cosine Law 18 18 9  05/07/2023 ------------- Units of Measure ------------- In conducting the process of measurement, it is necessary to define and use the proper unit of measure applicable for the quantity being observed. Correct conversion across different units of linear (distances, areas, volumes) and angular quantities is also imperative to maintain the accuracy of measurements. 19 19 ------ Units for Linear Measurements ------ In 1983, the Philippines adopted the Metric System or SI (International System), as its official system of measurements, phasing out the English System. Using SI, all linear measurements are based upon the ‘meter’. Thi s Photo by Unknown Author i s licensed under CC BY-SA 20 20 10  05/07/2023 ------ Units for Linear Measurements ------ Thi s Photo by Unknown Author i s licensed under CC BY-SA 21 21 --- Common Units for Linear Measurements --- Unit Abbreviation Kilometer km Meter m Centimeter cm Millimeter mm Square Meters m2 Cubic Meters m3 22 22 11  05/07/2023 --- Common Units for Linear Measurements --- Length Area 1 km 0.621371 mile 1 hectare 10,000 m2 1m 100 cm 1 hectare 0.01 km2 1 inch 2.54 cm 1 acre 4046.8564 m2 1 foot 12 inches 1 acre 4,840 yard2 1 yard 0.9144 meter Volume 1 yard 3 feet 1 m3 1,000,000 cm3 or cc 23 23 ------ Units for Angular Measurements ------ In the Philippines, angular measurements are expressed using the Sexagesimal System: the circle is divided into 360 degrees one degree ( ° ) is then divided into 60 minutes (’ ) one minute is further divided into 60 seconds (”) → Look for the [ ° ’ ” ] or [ D°M’S” ] or [ DMS ] button in your calculator 24 24 12  05/07/2023 Thi s Photo by Unknown Author i s licensed under CC BY-SA Thi s Photo by Unknown Author i s licensed under CC BY-SA Thi s Photo by Unknown Author i s licensed under CC BY-SA 25 25 Measuring and laying-out of an angle using a protractor Thi s Photo by Unknown Author i s licensed under CC BY-SA 26 26 13  05/07/2023 --- Common Units for Angular Measurements --- System Conversion Factors SI (Radian) 2π = 360 ° π = 180 ° Sexagesimal 1 ° = 60 ’ = 3600 ” (Degrees-Minutes-Seconds) 1 ’ = 60 ” 27 27 EXAMPLES Module 1 - Conversion of Units 28 28 14  05/07/2023 CONVERSION FACTOR Example: Convert 187.892 has. to square km. 1 hectare 0.01 km2 0.01 𝑘𝑚2 187.892 ℎ𝑎𝑠 × = 187.892 × 0.01 𝑘𝑚2 = 1.87892 𝑘𝑚2 1 ℎ𝑎 Example: Convert 2789.82 inches to centimeters and meters. in → cm 2789.82 𝑖𝑛 × 2.54 𝑐𝑚 = CONVERSION FACTOR 1 𝑖𝑛 1 inch 2.54 cm 2789.82 × 2.54 𝑐𝑚 = 7086.1428 𝑐𝑚 1m 100 cm cm → m 1𝑚 7086.1428 𝑐𝑚 × = 100 𝑐𝑚 7086.1428 𝑚/100 = 70.861428 𝑚 29 Example: Convert 12.5252 ° to DDD-MM-SS.SS format. → Input 12.5252 in your calculator and press =. → Press [ ° ’ ” ] or [ D°M’S” ] or [ DMS ] button to convert between decimal degrees and DMS format. → Press [ ° ’ ” ] or [ D°M’S” ] or 12° 31’30.72” [ DMS ] button again to convert back to decimal degrees 30 15  05/07/2023 ----------------- Basic Geometry ----------------- Geometric Terms: Point, Line Segment, Ray, Line, Plane, Angle Plane Figures and Solids Types of Lines Types of Angles Perimeter, Area, Volume Answer Module 1 Self-assessment Test to further recall the topics. 31 31 END OF LECTURE QUESTIONS? 32 32 16  05/07/2023 Prayer 33 33 17