Question

show that the ratio of the volume of a cylinder and a cone having same radius and height is 3:1​

Answer 1

Answer:

Step-by-step explanation:

Given,

Volume of cylinder = Volume of cone

=> π$r^{2}$h = 1/3 π $r^{2}h$

=> cancelling πr^2h on both sides,

We have ,

1 : 1/3

=> 3/1

=> 3:1

Hence the heights are in the ratio 3:1

••••

L.S.A of cylinder = 2πrh

T.S.A of cylinder = 2πr(r+h)

L.S.A of cone = πrl

T.S.A of cone = πr(l+r) where l is slant height.

Answer 2

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Given,

Volume of cylinder = Volume of cone

$=> πr^{2} = 1/3 π r^{2}hr$

=> cancelling $πr^2h$ on both sides,

We have ,

1 : 1/3

=> 3/1

=> 3:1

Hence the heights are in the ratio 3:1

••••

L.S.A of cylinder = $2πrh$

T.S.A of cylinder = $2πr(r+h)$

L.S.A of cone = $πrl$

T.S.A of cone = $πr(l+r)$ where l is slant height.