Question

if the radio of two cylinders are in the ratio 3:4and their heights are in the ratio 6:5 .find the ratio of their volumes

Answer 1

Answer:

27:40

Step-by-step explanation:

Given---> Radii of two cylinders are in the ratio 3:4 and their heights are in the ratio 6:5.

To find----> Let radii of cylinnders be r₁ and r₂ and heights be h₁ and h₂ .

ATQ, h₁ : h₂ = 6 : 5

Let, h₁ = 6h , h₂ = 5h

ATQ, r₁ : r₂ = 3 : 4

Let, r₁ = 3r , r₂ = 4r

Let volumes of cylinders be V₁ and V₂.

Now

Volume of cylinder = π r² h

Where , r = radius of cylinder

h = Height of cylinder

Volume of first cylinder = π r₁² h₁

V₁ = π ( 3r )² ( 6h )

= π ( 9 r² ) ( 6 h )

V₁ = 54 π r² h

Volume of second cylinder = π r₂² h₂

V₂ = π ( 4r )² ( 5h )

V₂ = π ( 16 r² ) ( 5h )

V₂ = 80 π r² h

V₁ / V₂ = 54 π r² h / 80 π r² h

= 54 / 80

V₁ / V₂= 27 / 40

=> V₁ : V₂ = 27 : 40

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Answer 2

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