Question

A cylinder and a cone have equal bases and equal heights.if their curved surface areas are in the ratio 8:5.the ratio of their radius and height is.

Answer 1

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Here's your answer.. ⬇⬇
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C.S.A of cylinder = 2πrh
C.S.A of cone = πrl

Given that both Radius and height are same of cylinder and cone.

Their C.S.A ratio is 8:5

C.S.A of cylinder/C.S.A of cone = 8/5
2πrh/πrl = 8/5
2h/l = 8/5
h/l = 4/5

Taking square on both sides..

( h/l )² = ( 4/5 )²

h²/l² = 16/25

h² 25/16 = l²

we know that l² = r² + h²

r² + h² = 25/16 h²

r² = 25/16 h² - h²

r² = 25/16 h² - 16h²

r² = 9/16 h²

r²/h² = 9/16

r/h = 3/4

Ratio of Radius and height is 3:4.
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Answer 2

Answer:

C.S.A of cylinder = 2πrh

C.S.A of cone = πrl

Given that both Radius and height are same of cylinder and cone.

Their C.S.A ratio is 8:5

C.S.A of cylinder/C.S.A of cone = 8/5

2πrh/πrl = 8/5

2h/l = 8/5

h/l = 4/5

Taking square on both sides..

( h/l )² = ( 4/5 )²

h²/l² = 16/25

h² 25/16 = l²

we know that l² = r² + h²

r² + h² = 25/16 h²

r² = 25/16 h² - h²

r² = 25/16 h² - 16h²

r² = 9/16 h²

r²/h² = 9/16

r/h = 3/4

Ratio of Radius and height is 3:4.