Math, asked by premkumar38, 1 year ago

the cylinder and cone have equal radii of their and equal height if their curved surface area in the ratio 8 :5 so that the reach of each is to height of each 3 upon 4

Answers

Answered by rishu6845

Given---> Cylinder and cone have equal radii and equal height and ratio of their curved surface area is 8:5 .

To show ---> Ratio of radius and height is 3:4 .

Solution---> Let radii and heights of cylinder and cone be r₁ , r₂ and h₁ and h₂ respectively.

ATQ, radii and heights of cone and cylinder are equal

So , r₁ = r₂ = r ( say ) , and h₁ = h₂ = h ( say )

Curved surface area of cylinder = 2 π r₁ h₁

=> S₁ = 2 π r h

Curved surface area of cone = π r l

=> S₂ = π r₁ l

We know that ,

l = √( r² + h² ) , applying it here we get,

=> S₂ = π r₁ √(r₁² + h₁² )

=> S₂ = π r √( r² + h² )

ATQ, S₁ : S₂ = 8 : 5

=> S₁ / S₂ = 8 : 5

Putting value of S₁ and S₂ , we get,

=> 2 π r h / π r √(r² + h² ) = 8 : 5

=> 2 h / √(r² + h² ) = 8 / 5

=> h / √(r² + h² ) = 8 / 2×5

=> h / √(r² + h² ) = 4 / 5

Squaring of both sides , we get,

=> h² / ( r² + h² ) = 16 / 25

=> 25 h² = 16 ( r² + h² )

=> 25 h² = 16 r² + 16 h²

=> 25 h² - 16 h² = 16 r²

=> 9 h² = 16 r²

=> r² / h² = 9 / 16

=> ( r / h )² = ( 3 / 4 )²

Taking square root of both sides we get,

=> r / h = 3 / 4

=> r : h = 3 : 4

=> Radius : Height = 3 : 4

#Answerwithquality

#BAL

Answered by Anonymous

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