CSA Ratio 1:2 Then V1 / V2 = ? | 1 Circular Sheet cut to 2 Cones | Math Doctor

A circular metallic sheet is divided into two parts in such a way that each part can be folded into a cone. If the ratio of their curved surface areas is 1 : 2, then the ratio of their volumes is (1) 1 : 8 (2) 1 : √6 (3) 1 : √10 (4) 2 : 3 This is Question 59 from Allen DLP - Solved by Math Doctor. CONCEPT: When a circular sector is folded into a cone: • Slant Height l = Radius R of original circle • Base Circumference 2πr = Arc Length of Sector • CSA of cone = π * r * l = π * r * R SOLUTION: CSA1/CSA2 = r1/r2 = 1/2 r1 = k, r2 = 2k Since full circle = both sectors, 2πR = 2πr1 + 2πr2 R = r1+r2 = 3k h = √(R² - r²) h1 = √(9k² - k²) = 2√2 k h2 = √(9k² - 4k²) = √5 k V = 1/3 πr²h V1/V2 = (k² * 2√2) / (4k² * √5) = 1/√10 Answer: V1/V2 = 1/√10 (Option 3) --- TOPICS: Mensuration - Circle to Cone, Sector, Curved Surface Area, Volume of Cone CLASS: Class 8, 9, 10, 11, 12 - Surface Areas and Volumes / Areas Related to Circles BOARDS: CBSE, ICSE, All State Boards, IGCSE, IB, NIOS - Common to all COMPETITIVE EXAMS: JEE Mains & Advanced, BITSAT, NTSE, IOQM, PRMO, IMO, SAT, SSC CGL, CAT, CUET, KVPY #MathDoctor #Mensuration #CircleTo2Cones #CSAToVolume #V1byV2 #Mensuration #OlympiadTrick #MathDoctor #SurfaceAreasAndVolumes #ConeTrick #Class10Maths #JEEMains #IOQM #CBSE #ICSE