Important Formulaes in Mesuration

Mensuration is one of the topics in Quants. Now a days questions coming from this chapter also. Here we are providing you Some important formulas which is used in mensuration which are useful in SSC, Railways and other exams.

Rectangle :

• Area = lb
• Perimeter  = 2(l+b)

Square :

• Area = a×a
• Perimeter = 4a

Parallelogram

• Area = l × h
• Perimeter = 2(l+b)

Triangle :

• Area =b×h/2 or √s(s-a)(s-b)(s-c)…………….where s=a+b+c/2

Right angle Triangle :

• Area =1/2(bh)
• Perimeter = b+h+d

Isosceles right angle triangle :

• Area = ½. a2
• Perimeter = 2a+d……………………….where d=a√2

Equilateral Triangle :

• Area = √3. a2/4 or  ½(ah)….where h = √3/2
• Perimeter = 3a

Trapezium :

• Area = 1/2h(a+b)
• Perimeter = Sum of all sides

Rhombus :

• Area = d1 × d2/2
• Perimeter = 4l

Quadrilateral

• Area =1/2 × Diagonal × (Sum of offsets)

Kite :

• Area  = d1×d2/2
• Perimeter  = 2 × Sum on non-adjacent sides

Circle :

• Area =  πr^2 or πd^2/4
• Circumference = 2πr  or πd
• Area of sector of a circle = (θπr^2 )/360

Frustum :

• Curved surface area = πh(r1+r2)
• Surface area = π( r12+ h(r1+r2) + r22)

Cube :

• Volume: V = l3
• Lateral surface area = 4a2
• Surface Area: S = 6s2
• Diagonal (d) = √3l

Cuboid :

• Volume of cuboid: lbh
• Total surface area = 2 (lb + bh + hl) or 6l2
• Length of diagonal =√(l^2+b^2+h^2)

Right Circular Cylinder :

• Volume of Cylinder = π r2 h
• Lateral Surface Area (LSA or CSA) = 2π r h
• Total Surface Area = TSA = 2 π r (r + h)
• Volume of hollow cylinder = π r h(R2 – r2)

Right Circular cone :

• Volume = 1/3 π r2h
• Curved surface area: CSA=  π r l
• Total surface area = TSA = πr(r + l )

Sphere

• Volume: V = 4/3 πr3
• Surface Area: S = 4πr2

Hemisphere :

• Volume = 2/3 π r3
• Curved surface area(CSA) = 2 π r2
• Total surface area = TSA = 3 π r2

Prism :

• Volume = Base area x h
• Lateral Surface area = perimeter of the base x h

Pyramid:

• Volume of a right pyramid = (1/3) × area of the base × height.
• Area of the lateral faces of a right pyramid = (1/2) × perimeter of the base x slant height.
• Area of whole surface of a right pyramid = area of the lateral faces + area of the base.

Tetrahedron :

• Area of its slant sides = 3a2√3/4
• Area of its whole surface = √3a2 
• Volume of the tetrahedron = (√2/12) a 3

Regular Hexagon :

• Area =  3√3 a2 / 2
• Perimeter  = 6a

Some other Formula :

• Area of Pathway running across the middle of  a rectangle = w(l+b-w)
• Perimeter of Pathway around a rectangle field = 2(l+b+4w)
• Area of Pathway around a rectangle field =2w(l+b+2w)
• Perimeter of Pathway inside a rectangle field =2(l+b-4w)
• Area of Pathway inside a rectangle field =2w(l+b-2w)
• Area of four walls = 2h(l+b)

Current Affairs Febuary 2017

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• Current Affairs Febuary 2017 

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• ·        UNICEF launches 3.3 bln USD to aid millions of Children.
• ·        Ireland became the world’s first country to stop investing in fossil fuels
• ·        Alibaba made app helps find 611 missing Children in China
• ·        Federal Judge temporarily blocks Trumph’s travel ban
• ·        World’s smallest Pacemaker unveiled in U.S.
• ·        Queen Elizabeth – II marks Sapphire Jubilee
• ·        Qatar Airways launches world’s longest commercial flight
• ·        China Becomes the World’s Largest Solar Power Producer
• ·        UK’s House of Commons Pases Brexit Bill
• ·        Sudarsan Pattnaik Creates World Record with Tallest Sand Sculpture
• ·        Neelu Rohmetra becomes first Woman Director of am IIM
• ·        Diego Maradona Gets Ambassador Role at FIFA 2017
• ·        Yo-Yo Ma and His ensemble win Best world Music Grammy
• ·        The International Aero India 2017 begins at
• ·        India’s first dedicated heliport in New Delhi.
• ·        Dustin Johnson dominates Genesis Open to overtake World No.1
• ·        Mumbai Named Richest Indian city with Total Wealth $ 820bn
• ·        H1B and L1 reform Bill introduced in US House of Representatives
• ·        India ranks 43rd in USCC’s IP Index
• ·        Shawna Pandya Third Indian origin woman to go to space
• ·        Indian cycle tourist establishes a Guinness World Record
• ·        India to host maiden ITTF World Tour event in February
• ·        India, UK signed bilateral MoU to allow more flights to boost tourism and trade
• ·        Union Govt signs agreement with Croatia on economic Cooperation
• ·        Norman Isaac became first Indian to be FIBA’s Technical Delegate
• ·        Govt appoints 5 new Judges to Supreme Court
• ·        IMF opens technical centre in New Delhi
• ·        India as the World’s Largest Arms Importer
• ·        India, Japan ink pact on Rail Safety
• ·        India clears a mega missile deal with Israel
• ·        World’s First Robot Table Tennis Tutor sets new Guinness World Record
• ·        E-paathsala launches technology-backed services for higher education institutions in India
• ·        .
• ·        Jaitley unveils education reforms, to set up National Testing Agency
• ·        Rail Museum celebrates 40th anniversary
• ·        Govt, forms panel to improve Haj Policy
• ·        Health Ministry launches Measles-Rubella Vaccine (MR) Campaign
• ·        Chief Minister Samagra Gramya Unnayan Yojana (CMSGUY) launched in Assam
• ·        Muslim Organisations to oppose triple Talaq as is practiced now low panel
• ·        Indian Railways Approves Rail Project in Andaman and Nicobar
• ·        Indian Navy launches Underwater Harbour Defence and Surveillance system
•  
• ·        SC Clears plan to Verify mobile phone users through Aadhar
• ·        Cabinet approves Pradhan Mantri Gramin Digital Saksharta Abhiyan
• ·        RBI setup panel on strengthening cyber security
• ·        Govt appoints 3 directory to RBI Central Board
• ·        Govt to make “Aadhar” compulsory to ration from PDS shops
• ·        Govt to open 56 Post Office passport Seva Kendra facilities
• ·        .
• ·        Kerala’s Nilambur teak to get GI tag
• ·        GMR Hyderabad Airport bags CAPA award
• ·        China releases theme, priorities of BRICS
• ·        INS sarvekshak installs solar Power System.
• ·        Sachin Tendulkar adopted Donja Village for Development
• ·        Food grain Production to reach record 272 million tonnes in 2016-17
• ·        ‘Science Express’ Train Flagged off from New Delhi
• ·        UAE Unveils Plan to Build First City on Mars by 2117
• ·        Delhi AIIMS wins first prize for sanitation
• ·        INSV Tarini inducted into Indian Navy
• ·        Virat Kohli first Indian sports person to ink Rs.110-crore deal with Puma
• ·        Ravi Shanka Prasad launches Cyber Swachhta kendra in New Delhi
• ·        SC Judge appointed as Chairman of Cauvery Water Disputes Tribunal
• ·        Union Government launches Bharat QR code
• ·        Govt doubles maternity leave for women workers in Industries
• ·        Suresh Prabhu Unveils Antyodaya Rail Coaches
• ·        Telangana, Rajasthan bag eGov awards
• ·        2% reservation to sports persons in Govt Jobs CM. Raghubar Das
• ·        Telangana launches India’s first social innovations hub
• ·        First smart Police Station inaugurated in Andhra Pradesh
• ·        Gujarat becomes first cashless state for PDS
• ·        National Women’s Parliament begins in Andhra Pradesh
• ·        NCS and Jeevan Pramaan Facility for EPFO Pensioners Launched in Hyderabad
• ·        Supreme Court convicted Sasikala in disproportionate assets case
• ·        Kerala Govt gave approval for Airport in Sabarimala
• ·        Palaniswami takes oath as TM CM along with 30 ministers
• ·        Maharashtra Approves Rs. 250 crore Cloud Seeding Programme
• ·        31st State Hood Day of Arunachal Pradesh and Mizoram 20 February
• ·        Germany Opens Consulate Office in Hyderabad
• ·        National Biodiversity Congress 2017 in Kerala
• ·        Rajasthan becomes 2nd Largest Crude Oil Producer in India
• ·        Vasundhara Raje inaugurates Medical project RAHAT
• ·        A 3-day global nuclear security meet in New Delhi.
• ·        Indian seed congress-2017 in Kolkata
• ·        2017 Mobile World Congress (MWC) Begins in Barcelona
• ·        Alastair Cook awarded Order of the British Empire
• ·        Indian – Origin British Sculptor Anish Kapoor wins $ 1 Million Israeli Prize
• ·        Hyderabad Surgeon Raghu Ram Honoured with BC Roy Award
• ·        Indian Tabla player Sandeep Das wins 2017 Grammy Award
• ·        Adele sweeps top prizes at 2017 Grammy Awards
• ·        Usain Bolt wins Laureus “Sportsman of the year” award
• ·        Jawaharlal Nehru University Won Visitor’s Award
• ·        Hindi Scholar and Writer Surendra Verma selected for Vyas Samman 2016 Award
• ·        Corporation Bank Bags 2017 National MSME Excellence Award
• ·        Lata Mangeshkar honoured with Legendary Award
• ·        ‘Newton’ wins top honour at Berlin Awards
• ·        Katamati Iron Mine Wins Best Green Award
• ·        Milind Soman gets the title Ultraman
• ·        Oscar Awards 2017 Lala Land won maximum awards
• ·        Shooting World Cup India bag 1Gold, 1 Silver Medals
• ·        Pankaj Advani wins National Snooker Championship title
• ·        Lakshya Sen becomes World No.1 Junior Badminton player
• ·        Virat Kohli features on Wisden 2017 cover
• ·        Iran Lifts ban on American Wrestling team
• ·        Sourabh Varma Clinches Men’s Single title in NBC
• ·        India to host FIBA Women’s Asic Cup
• ·        India’s first centre for disabled sportsmen in Gandhinagar
• ·        Delhi Mohit Ahlawat becomes first batsman to score 300 in T-20 Cricket
• ·        Kohli get a new record for most Test 150 s by an Indian Captain
• ·        Mission XI Million launched to promote football among school Children
• ·        Official mascot of FIFA U-17 World Cup Kheleao
• ·        India win T-20 Blind World Cup – 2017
• ·        R. Ashwin becomes Fastest Bowler to claim 250 wickets
• ·        Joe Root Becomes New Test Captain of England
• ·        De Randamie Crowned First Women’s Featherweight Champion.
• ·        Jehan Daruvala wins New Zealand Grand Prix
• ·        Indian Hockey player To Get Honorary Doctorate
• ·        PV Sindhu Attains Career-Best Rank at No.5
• ·        22 Football Players & Officials Gets life Ban.
• ·        Jo-Wilfried Tsonga wins 2017 Rotterdam Open
• ·        India win Silver at Asian Women’s Rugby Sevens Trophy
• ·        Ben Stokes gets highest bidding at IPL auction
• ·        India to host 2019 combined World Cup for Shooting
• ·        Mithali Raj, Harmanpreet kaur in top -10 ICC rankings
• ·        Dohmen, Navomi named best hockey players of 2016
• ·        ISSF World Cup Pooja Ghatkar gets Bronze
• ·        R Aswin Breaks Kapil Dev’s Record to become Highest Test Wicket Taker
• ·        Saina Nehwal to represent Olympic Committee in BWF
•  
• ·        ECONOMY
• ·        Arun Jaitley introduced Economic Survey 2016-17 in Parliament
• ·        Highlights of Union Budget 2017-18
• ·        For quick refund of tax returns time-frame reduced to 12 months
• ·        Of 76 lakh individuals who reported income of over Rs 5 lakh, 56 lakh are salaried
• ·        No transaction over Rs 3 lakh will be permitted in cash
• ·        To cut presumptive turnover threshold for companies w/turnover up to Rs 2 cr to 6%
• ·        Basic customs duty on LNG cut to 2.5% from 5%
• ·        Propose to reduce tax for small companies with turnover of < Rs 50 cr to 25%
• ·        Govt proposes carry-forward of MAT to 15 years from 10 years
• ·        Post demonetisation deposits between Rs 2.80 lakh made in 1.09 crore accounts
• ·        FY18 revenue deficit pegged at 1.9% of GDP
• ·        Fiscal deficit for 2017-18 pegged at 3.2%, in-line with market expectations
• ·        Defence capital expenditure: Rs 86,000 core
• ·        New FDI policy under consideration
• ·        Aadhaar Pay will be launched shortly
• ·        Propose revised mechanism for time-bound listing of PSUs
• ·        Govt doubles lending target of banks to Rs 2.44 lakh cr
• ·        Amend Negotiable Instruments Act to protect payees of dishonoured cheques
• ·        Govt to take steps to promote digital payments at petrol pumps, hospitals
• ·        Propose to create a payment regulatory board at RBI
• ·        Propose to create an integrated oil major
• ·        Budget 2017: Focus on welfare, infra with fiscal prudence
• ·        Service charges on e-tickets booked via IRCTC to be withdrawn
• ·        New Metro Rail policy to be announced; will open up new job possibilities.
• ·        New rules for pricing medical devices should benefit common man.
• ·        Railways to implement end-to- end solutions for some commodities.
• ·        Propose to feed 7000 solar railway station in medium term
• ·        2000 km of coastal roads have been identified for development.
• ·        AAI Act to be amended to enable monetisation of land.
• ·        Cash less reservation have improved to 68% from 58%.
• ·        National highway allocation at Rs 64,000 crore
• ·        Affordable housing to be given infra status
• ·        Have hiked allocation for women skill development to Rs 1.84 lakh crore in FY18.
• ·        Mahila Shakti Kendras will aim for Woman Empowerment
• ·        Govt to set up 100 India-International skill centres
• ·        Mahila Shakti Kendra will be set up at village level; allocation Rs 500 crore
• ·        5 special tourism zones to be set up in partnership with states
• ·        Unmanned Rail level crossing will be eliminated by 2020
• ·        At least 25 stations re-development contracts will be awarded in 2017-18.
• ·        Propose to invest Rs 1.31 lakh crore in Railways in 2017-18.
• ·        Total capital development outlay for Railway at Rs 1.3 lakh cr.
• ·        Railways to implement end-to- end solutions for some commodities
• ·        Propose to feed 7000 solar railway station in medium term
• ·        Railway throughput to be enhanced by 10%.
• ·        Pilot project for Aadhar cards containing health details for senior citizens.
• ·        Govt to undertake reforms in UGC to improve higher education.
• ·        New rules regarding medical devices will be formulated; will attract investment in sector, will reduce cost of the devices
• ·        Outcome-based monetary measures to SC, ST by NITI Aayog
• ·        Allocation to scheduled castes upped to Rs 52,393 crore
• ·        Govt to set up 100 India-International skill centres
• ·        Outcome-based monetary measures to SC, ST by NITI Aayog
• ·        Govt committed to ensuring conducive labour environment
• ·        Will take legislative reforms to simplify labour laws in India
• ·        Govt committed to take structural reform in medical education & practice
• ·        Propose to amend drug rules to ensure drugs available at reasonable prices
• ·        1.5 lakh health sub-centres to be transformed to health wellness centres
• ·        Will encourage reputed hospitals to start courses
• ·        Affordable housing to be given infra status
• ·        Bank lending rates for housing loans coming down in wake of demonetisation, says FM
• ·        58.Innovation fund for secondary education to be created
• ·        Sanitation coverage in rural areas risen to 60% vs 42% earlier
• ·        On our way to achieve 100% village electrification by 1st May 2018
• ·        Govt to achieve 100% rural electrification by May 1, 2018
• ·        Rs 4,800 crore allocated under Deen Dayal Upadhyaya Gram Jyoti Yojana
• ·        Propose to finish 1 crore houses by 2019 for those living in kachcha houses
• ·        To up crop insurance coverage to 50% in FY19
• ·        Pace of construction of roads has increased to Rs 133 km/day in 2017
• ·        Long-term irrigation fund set up in NABARD, additional corpus Rs 20,000 cr
• ·        MNREGA target at 48000 cr in FY18
• ·        Participation of women in NREGA has increased to 55% from 48% in the past.
• ·        Govt to set up dairy processing fund
• ·        Pace Of Construction Of Roads Has Increased To Rs 133 Km/Day In 2017
• ·        Pradhan Mantri Gram Sadak Yojana construction at 133 km per day now against 73 km per day earlier
• ·        Increased allocation to Rs 23,000 crore for PM Awas Yojana,
• ·        19000 cr allotted for PM Rural road plan in FY18
• ·        Will undertake reforms in UGC to improve higher education
• ·        Total allocation for rural sector up by 24% at Rs 1,83000 cr.
• ·        Allocation for rural, agri & allied industry at Rs 1.87 lakh crore, up 24% YoY
• ·        Coverage of national agriculture market will be expanded.
• ·        Dairy processing infra fund will be created with corpus of Rs 8,000 crore in 3 yrs
• ·        Long term irrigation fund set up in NABARD, additional corpus Rs 20,000 cr
• ·        Will support NABARD to digitise 63,000 primary agri co-operatives
• ·        5000 cr worth dedicated micro irrigation fund to be set up by NABARD
• ·        Will take steps to make sure farmers get better prices for harvest
• ·        Sowing farmers should feel secure against natural calamities
• ·        To up crop insurance coverage to 50% in FY19
• ·        Will ensure flow of adequate credit to under privileged areas
• ·        Committed to double farmer income in five years
• ·        Propose to present Budget under 10 district themes
• ·        Agriculture expected to grow at 4.1% in the current year
• ·        Target for agri credit fixed at Rs 10 lakh crore this year
• ·        Overall approach has been to spend more with fiscal prudence
• ·        Looking to spend more on rural infrastructure and social spending
• ·        Overall approach in Budget has been to spend more in rural areas
• ·        Have done away with planned & unplanned allocation
• ·        Merger of Rail & General Budget is a historic step
• ·        IMF estimates world GDP will grow by 3.4% in 2017
• ·        Govt reduces existing tax rate for personal income of Rs 2.5-5 lakh to 5% from 10%
• ·        Govt proposes Payments Regulatory Board in RBI
• ·        Rs.10,000 penalty for late filing of IT returns
• ·        Sunil Mehta has been appointed as the Non Executive Chairman in Punjab National Bank

·        .

·        SCIENCE & TECHNOLOGY

1. ·        SAARC programming committee meeting Held in Kathmandu
2. ·        Scientists confirm multiple therapeutic properties of Neuro Calyx Calycinus
3. ·        Horse Antibodies may effectively treat Ebola
4. ·        Earth like planet “Proxima b” Unlikely to host life
5. ·        ISRO creates a World record With 104 Satellites in One go
6. ·        Scientists Are Getting Really Close to a Malaria Vaccine
7. ·        Scientists Create Graphene from Soybeans
8. ·        Scientists discover a Continent Zealandia
9. ·        7 New Earth – Like Exoplanets Discovered
10. ·        7 Tiny New Frogs are Discovered in India
11. ·        NASA may send robotic spacecraft to sun in 2018

·        PERSONS IN NEWS

1. ·        A). APPOINTMENTS
2. ·        Ashok Amritraj Appointed as UN in India Goodwill ambassador
3. ·        Alok Verma joined as the new CBI Director
4. ·        Arun Kumar elected as Chairman and CEO of KPMG in India
5. ·        Jovenel Moise Sworn in as Haiti’s new President
6. ·        Mohamed Abdullahi Farmajo elected as Somalia’s New President
7. ·        Hemant Bhargava appointed LIC’s MD
8. ·        Govt Appoints Ajay Tyagi As New SEBI Chief
9. ·        Frank-Walter Steinmeier elected President of Germany.
10. ·        Sandeep Jajodia takes over as ASSOCHAM President
11. ·        Narinder Chauhan appointed as Ambassador of India to the Republic of Philippines
12. ·        Jean-Pierre Lacroix appointed as new UN Peacekeeping Chief
13. ·        Nilesh Shivji Vikamsey as new ICAI President
14. ·        Justice Vikramjit Sen takes charge of DDCA
15. ·        K. Palaniswami to Be Sworn in as Tamil Nadu Chief Minister
16. ·        Vikas Swarup as High Commissioner of India to Canada
17. ·        Neelam Damodaran is Bank of India new ED
18. ·        Nanda Kumar Sai Appointed as Chairman of NCST
19. ·        Trump Appoints HR McMaster as National Security Adviser
20. ·        Turbohelize Liezietsu as Nagaland New CM
21. ·        Chandrasekaran takes the Chairmanship of TATA Sons Ltd
22. ·        Abhijit Sarkar appointed Vice President of AHF
23. ·        Shilpa Shetty as Swachh Bharat Brand Ambassador
24. ·        Former CM TR Zeliang Appointed Finance Advisor To Nagaland Govt
25. ·        Khursheed A Ganai appointed as CIC of Jammu & Kashmir
26. ·        Gopal Baglay Appointed External Affairs Ministry Spokesperson

·        B). RESIGNS

1. ·        Alastair Cook steps down as England Test Captain
2. ·        US National Security Adviser Michael Flynn resigns.
3. ·        Nagaland CM TR Zeliang resigned
4. ·        BCCI General Manager RP. Shah resigned his post

·        C). DEATHS

·        Veteran Journalist Dileep padgaonkar died at 72

1. ·        Former Minister E Ahamed Dies After Suffering Cardiac Arrest 
2. ·        Ex-CBI Director Joginder Singh passes away
3. ·        Renowned Urdu Author Bano Qudsia Passes away
4. ·        Veteran freedom fighter Racharla Samrajyam passes away        
5. ·        Netaji’s driver Colonel Nizamuddin passes away
6. ·        Japanese manga legend Jiro Taniguchi dies at 69
7. ·        Eminent Journalist and Laughter Persona Pandit Dharmsheel Chaturvedi Dies 
8. ·        Nobel Laureate Sir Peter Mansfield Passes away
9. ·        Veteran Indian Journalist T.V. Parasuram passes Away
10. ·        Former CJI Altamas Kabir passes away
11. ·        Celebrated Hindi Novelist Ved Prakash Sharma Passes away
12. ·        Former Union Minister P.Shiv Shankar passes away
13. ·        Nobel Winning Economist Kenneth J.Arrow dies at 95
14. ·        Shahabuddin Ahmed invited as in Residence guest
15. ·        hajuraho Dance Festival to be begin in Madhya Pradesh

·        BOOKS IN NEWS

·        Salman Rushdie’s novel “The Golden House” announced

·        COMMITTEES

1. ·        Norway Nobel Committee Chairwoman Kullmann Dies At 65
2. ·        World Cancer Day 2017: 04 Feb 2017
3. ·        International Day of Women and Girls in Science
4. ·        13th February-World Radio Day
5. ·        International Mother language Day-February 21
6. ·        74th Central Excise Day Celebrated on 24 February
7. ·        Chandra Shekhar Azad’s martyrdom day observed on 27 February
8. ·        National Science Day 28th February