Math, asked by jackzzjck, 6 months ago

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

Answers

Answered by knjroopa

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

Answered by challengerop

Answer:

ya the above answer is correct

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