by Catacutan, Cressa Y.; Lomentigar, Divina Mae M. & Luis, Carmina Janellie C.
Pyramids and cones are kinds of solids in geometry. Solid Geometry is the geometry of three-dimensional space. Why three-dimensional? It is called such since there are three-dimensions which are the width, depth and height.
There are two major types of solids, Polyhedron and Non-Polyhedron. Polyhedron has flat faces and straight edges. On the other hand, a non-polyhedron has one or more of its sides curved.
So in which of the two groups of solids do you think pyramids and cones belong? Do they belong on the same group? or not? If you can't distinguish don't worry, as we go on this topic it'll be sure easy for you.
So let us first talk about pyramids...
Pyramid, when people hear
the word maybe the first thing that would be in mind is Egypt, where the great pyramids are located. But what if we are ask to find the
area of those? Don't worry! With these simple steps and formulas,
it's easy.
But first what is a
pyramid in geometry?
A pyramid
is a three-dimensional solid and it is a polyhedron. Its base is a polygon and its
sides are triangles which intersect in one point called the vertex. There are different types of pyramids. They are called according to
the shape of their bases. Like square pyramid(square) &
triangular pyramid(triangle). There are also regular pyramids which
consist of congruent sides.
These are the formulas
and symbols used in finding the surface area of a pyramid:
SA= Surface Area
l= slant height
B =
Area of the base (Depends on the formula of the shape of the base)
P=
Perimeter
Slant
height:
l ² = h² + (1/2side)²
l ² = h² + (1/2side)²
Surface
Area:
SA
= B+ 1/2Pl
Example:
1. Identify what was asked to find. (In this case, of course, we are to find the surface area of this pyramid)
2. Identify the given values.
---> l=12cm; L=6cm; W=6cm
---> l=12cm; L=6cm; W=6cm
3. Identify the formula. (Note: If the slant height is not given you have to use the slant height formula first to find it before proceeding in using the formula in finding the surface area of a pyramid)
---> SA = B+ 1/2Pl; S²=Area of square base
---> SA = B+ 1/2Pl; S²=Area of square base
4. Substitute the given values to the formula.
---> SA = 6² + 1/2(6x4)(12)
---> SA = 6² + 1/2(6x4)(12)
5. Perform the indicated operations.
---> SA= 36 + 1/2(24)(12) = 180cm
---> SA= 36 + 1/2(24)(12) = 180cm
6. If you got a decimal answer, You may round off your answer to the nearest whole number if said in the instructions. Tip: Box or encircle your answer & don't forget to put the proper unit.
See? It's just as easy and fun as touring around the great pyramids..
Now let's move on to the world of cones..
If people
would be reminded of Egypt whenever they hear the word 'pyramid',
what do you think would come in their minds if they hear the word
“cone”?
Of course, nothing else but Ice cream! Simply because of
its cone. Again, what if we are ask to find the area of the ice cream
cone that we are holding? It's just easy as eating ice cream as long
as you follow these simple steps and formulas.
What is a cone in
geometry?
A Cone
is a three-dimensional solid in which its base is a circle. Its sides
are formed by straight lines connected to the circular base to a
vertex. The perpendicular distance from the vertex to the center of
the base is the height.
These are the formulas and symbols used in finding the surface area of a cone:
SA
= Surface Area
l=
Slant height
B=
Area of base (Area of a circle= πr²)
r=
radius
h= height
π =3.14
h= height
π =3.14
Slant
height: l
²
= r² + h²
Surface
Area:
SA
= B + π rl
Example:
1. Identify what was asked to find. (In this case, of course, we are to find the surface area of this cone)
2. Identify the given values.
---> h= 14cm; r= 4cm
---> h= 14cm; r= 4cm
3. Identify the formula. (Note: If the slant height is not given you have to use the slant height formula first to find it before proceeding in using the formula in finding the surface area of a pyramid)
---> l ² = r² + h²
---> SA = B + π rl; (Area of a circle= πr²) ---> SA= πr²+ π rl
---> l ² = r² + h²
---> SA = B + π rl; (Area of a circle= πr²) ---> SA= πr²+ π rl
4. Substitute the given values to the formula.
---> l ²= (4²) + (14²)
---> SA = (3.14)(4²)+ (4)(15)
---> l ²= (4²) + (14²)
---> SA = (3.14)(4²)+ (4)(15)
5. Perform the indicated operations.
---> l ² = 16 + 196
= √212
= 14.56 = 15
---> SA= (3.14)(4²)+ (3.14)(4)(15)
= 50.24 + 188.4
= 238.64 = 239cm
---> l ² = 16 + 196
= √212
= 14.56 = 15
---> SA= (3.14)(4²)+ (3.14)(4)(15)
= 50.24 + 188.4
= 238.64 = 239cm
6. If you got a decimal answer, You may round off your answer to the nearest whole number depending on the instructions given. Tip: Don't forget to put the proper unit.
After all these simple formulas and steps to follow I'm sure computing for the surface areas of pyramids and cones are now easy as eating ice cream. Of course don't forget that the best way to learn Mathematics is to keep on practicing solving problems & equations.
Thank you all and Have a fun math filled life! Hope you learned a lot :)
To test what you have learned here are some exercises:(Please try to answer first. Do not peek on the answer key)
1.
2.
3.
4.
5.
Credits to Mr. Crisencio M. Paner who inspired us to do this blog in order to share our knowledge to the world.
*Here's our respectable professor's curriculum vitae
CRISENCIO M. PANER
CP : 0915-1429675 Email : panercris@gmail.com
EDUCATION
- Ph.D. in Biological Science (candidate)
University of Santo Tomas, Graduate School
- M.S. Microbiology
University of Santo Tomas
Thesis: “Chemical Control of Fungi Infesting Easel Oil Paintings at
University of Santo Tomas Museum of Arts and Sciences”
- Italian Scholarship Grant
Restoration and Conservation of Artworks Attacked by Biological Agents
Istituto Centrale Per Il Restauro, Rome, Italy (January 1-June 30, 2004)
- B.S. Biochemistry
University of Santo Tomas
- Professional Teaching Certification Program (Major in Biological Science)
Caloocan City Polytechnic College
PUBLICATIONS
Book:
Co-author in LET Reviewer in Biology, 2006-2010 eds. Published by MET Inc.
ISBN # 97193249-6-1, sold in National Bookstores
Articles:
- Understanding Museum Pests: The Molds. CFAD Atelier Journal, University of Santo Tomas, Vol. 2 No. 1, 2003-2004, pp. 80-83
- On the Conservation of 20th Century Color Photographs Attacked by Molds. CFAD Atelier Journal, UST., Vol. 2 No. 1, 2003-2004, pp. 106-113
- Witnessing the Glory of Italy in Its Art History and Ancient Spaces. CFAD Atelier Journal, UST, Vol. 3 No. 1, 2004-2005, pp. 55-72
- _______________. Panorama Magazine, November 13, 2005, pp. 12, 13, & 21.
- Deterioration of Paintings and Painting Components Caused by Microorganisms. CFAD Atelier Journal, UST., Vol. 3 No. 1, 2004-2005, pp. 91-94
- Microbial Deterioration of Painting Materials. CFAD Atelier Journal, UST., Vol. 3 No. 1, 2004-2005, pp. 94-97.
- Conservation of Paintings Attacked by Molds. In College Freshman English Book II. Agalabia, U., Aranda, R., et. al., pp. 124-125, UST Publishing House, 2004
- Today’s Restoration Establishments. CFAD Atelier Journal, UST., Vol. 4 & 5 No. 1, 2005-2006 & 2006-2007, pp. 95-99
RESEARCH WORK
- Indoor Air Quality of Beato Angelico Building of the University of Santo Tomas -Commissioned by UST (Nov. 2009-May 2010)
WEBSITES/BLOGS
- http://internet-moneymakingsecrets.blogspot.com
- http://internet-moneymakingsecrets.weebly.com
- http://cmpaner.blogspot.com (The Painting Doctor-“Restorer/Conservator”)
- http://sulit.com.ph/3498047 (Research assistance/Thesis Assistance/Thesis Editing)
- http://sulit.com.ph/4829772 (LET Review by a LET Topnotcher and Veteran Reviewer)
- http://sulit.com.ph/5040331 (Lotto Secrets Revealed!)
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- http://sulit.com.ph/4186306 ( Art and Craft Materials)
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- http://sulit.com.ph/4802983 (LET Reviewer Books)
- http://sulit.com.ph/5021693 (Lose Weigh Program & Stop Hair loss Program)
WORK EXPERIENCE
- Instructor 5, CFAD, IPEA, Pharmacy, CTHM, University of Santo Tomas
SY 1995-Present
Subjects taught: Organic Chemistry lab., Statistics, College Algebra,
Algebra with Trigonometry, Business Math, Physics,
Plane & Solid Geometry, Environmental Science, Biology
- Part Time Instructor, Our Lady of Perpetual Help College, Manila
Subjects taught: Food Microbiology (Lecture and Laboratory)
- Part Time Instructor, St. Paul’s College, Quezon City
Subjects taught: Lec. & Lab: General Microbiology, Biochemistry, Microtechnique
- Part Time Instructor, Unciano Colleges and General Hospital, Inc., Manila
Subjects taught: Lec. & Lab: General Microbiology and Parasitology, Inorganic Chemistry,
Comparative Anatomy, Botany, Organic Chemistry, General Zoology,
Biology, Biochemistry
OTHER PROFESSIONAL EXPERIENCE
- Editor and Professional Consultant, MET Publishing House, Manila
- Microbiologist, Silver Swan Manufacturing Inc.,Panghulo, Malabon
- Biochemist, Watercare Philippines, Inc., Valenzuela City
- Food Production Researcher(Mushroom Culture), TWH, Inc., Cainta Rizal
- Review Director for LET, Center for Educational Excellence, Inc.
- Project Consultant on “Biodeterioration of Artworks”, Paper Conservation Laboratory, Archives Dept., Arzobispado de Manila
Projects: Conservation of paintings by Fernando Amorsolo, Botong Francisco,
Ben Cab, Cezar Legaspi, Simon Flores, Betsy Westerndorp
- Licensure Exams For Teachers (LET) Reviewer at:
- Malabon City University,MET Review Center, UST-College of Education, Caloocan Polytechnic College, Trinity College, & Center for Educational Excellence Inc.
AWARDS AND HONORS
- 10th Placer (85.60%), Licensure Examinations for Teachers (LET)
- Full College Scholarship by Lourdes Reyes Foundation
- Professional Civil Service Examinations, weighted ave: 86.49%
- Valedictorian, High School
- Salutatorian, Elementary
- Certificate of Appreciation as resource speaker on the topic “Visual Arts and Restorations”, Faculty-Student Art Forum, Beato Angelico Bldg.,UST.
- Recognition Award for invaluable support and committed service to HARIBON UST as adviser from 2002-2004
- Honored as 4th Degree(highest degree) member of the Knights of Columbus
Given by Philippine District IV-NCR
- Loyalty and Faithful Award for 13 years of Service
Knights of Columbus UST- Faculty Council 4321
- Dedicated and Competent Service Award as LET Reviewer
Malabon City University
- Champion, Pautakan Quiz Bee for Coaches, UST
- Family of the Year Award
Knights of Columbus UST Faculty Council 4321
- UST Graduate School Thesis Writing Grant
UST Graduate School Alumni Association
- Certificate of Recognition for invaluable Contribution as Lecturer/Reviewer
Pilot Project on Review Classes for Licensure Examinations for Teachers
College of Education, UST
- Certificate of Appreciation as guest speaker on the topic “Products that Cause Cancer”, given by NEWAYS International (Phils.), Makati City
TRAINING /SEMINAR WORKSHOPS
- Seminar on Test and Measurement Evaluation
- Seminar on Principles/Philosophy of Education
- Faculty Development Seminar
- Traditional Filipino Art
- Curriculum Development
- Rubrics Development Across Disciplines
- Certificate on Adobe Photoshop
- Certificate on PC Troubleshooting and Networking
- The Ethics of Teaching
- Rights and Responsibilities of the Faculty Members, Academic and Administrative Officials and Office Staff Seminar
- UST-CFAD Planning and Development Seminar
- Shepherding the Shepherds
- Workshop on Syllabus Construction
- Textbook and Learning Materials Development
- Computer Literacy on Adobe Illustrator, Photoshop, & MS Excel
- Symposium on Waste Management
- Ecological Symposium
- Bringing Out the Best in Me and the Best in You
- Integrating Media in Classroom Instruction( Design, Production, and Utilization of Media)
- Principles and Methods of Humane Educators
- Certificate on Basic Industrial Electronics
- Certificate on Information Technology
- Symposium on the Preservation of our Environment
- Research Colloquia on Indoor Air and Water Quality in Relation to Building Design
- Convention of Philippine Association of Academic Biochemists,
- 16th Annual Convention of Philippine Biochemical Society
- Script Writing Workshop
- Basic Business and Financial Management
AFFILIATIONS
- Member, CFAD- Adhoc Committee on Math Department
- Member, CFAD-Adhoc Committee on Value Formation
- Board of Director
Philippine Association for the Scientific Conservation of Cultural Properties
- Deputy Grand Knight, Knights of Columbus UST Faculty Council No. 4321
- Auditor
College of Fine Arts & Design Faculty Association
- Adviser, HARIBON UST
- Business Manager, NOH-SCC Alumni Association
- Member, Outreach Program Committee
College of Architecture and Fine Arts
LANGUAGES SPOKEN
English, Filipino
OTHER SPECIAL SKILLS/TALENTS
- Computer operation using MS Word, Excel, Powerpoint, Adobe Photoshop, Internet
- Computer Hardware repair and Software installations
- Website/Blog Construction
- Photography
- Swimming
- Playing Banduria
- Singing
- Riding ATV
*You may also check our profile
References:
- Pyramids and cones. Retrieved from http://www.algebralab.org/lessons/lesson.aspx?file=geometry_3dpyramidcone.xmlSolid Geometry. Retrieved from http://www.mathsisfun.com/geometry/solid-geometry.html
- Surface area of pyramids and cones. Retrieved from http://www.sophia.org/packets/surface-area-of-pyramids-and-cones--3
- Image retrieved from: http://www.mathsisfun.com/geometry/images/pyramid-height-perimeter.jpg
- Image retrieved from: http://www.mathsisfun.com/geometry/images/cone-dimensions.jpg
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