Question

a circular metallic sheet is divided into two parts in such a way that each part can be folded into a cone IF RATIO OF THEIR CSA IS 1:2 FIND RATIO OF THEIR VOLUME PLEASE ONLY CORRECT ANSWERS

Answer 1

Step-by-step explanation:

Given a circular metallic sheet is divided into two parts in such a way that each part can be folded into a cone IF RATIO OF THEIR CSA IS 1:2 FIND RATIO OF THEIR VOLUME  

• So a circle is divided into two parts like theta and 360 – theta.
• Now let a circle PQRS be divided into 2 parts like PSQ and PRQ
• Area of sector PSQ / Area of sector PRQ  
• theta / 360 x πr^2 / 360 – theta / 360 x π r^2 = ½
•        theta / 360 – theta = 1/2  
•      2 theta = 360 – theta
•  Or theta = 120 degree
• Now PSQ = theta / 360 x circumference
•                 = 120 / 360 x 2 π r
•            = 2/3 π r
• Also PRQ =4/3 π r
• Now each part is folded into a cone
• SO PSQ = circumference of base = 2πr1
•                    2πr/3 = 2πr1
•               So r1 = r/3
• Similarly we have
•                  4πr/3 = 2πr2
•            So r2 = 2r/3
• Now we need to find the height
•          So h1 = √r^2 – r1^2
•                    = √r^2 – r^2/9
•                  = 2√2 r / 3
•       So h2 = √r^2 – r2^2
•               = √r^2 – 4r^2 / 9
•            = √5 / 3 r
•     Volume will be 1/3 πr^2 h
• Now volume v1 / v2 = 1/3 π r1^2 h1 / 1/3 π r2^2 h2
•                                       = (r1/r2)^2 (h1/h2)
•                                      = (r/3 / 2r/3)^2 (2√2 / 3 /√5 / 3r)
•                                      = 1/4 x 2√2 / √5
•                                    = 1/√10
•     So we get v1: v2 = 1 :√10

Reference link will be

https://brainly.in/question/19419943

Answer 2

Answer:

ya the above answer is correct