Question

a cylinder and a cone have equal height and equal radii of their bases. if their csa are in the ratio 8:5. show that their ratio of radius to height of each is 3:4.

Answer 1

Let the radius and height of cylinder and cone be r and h. 
Let the slant height of cone be l. 

CSA of cylinder : 2πrh
CSA of cone : πrl

Ratio = CSA of cylinder/CSA of cone = 2πrh/πrl = 8/5

⇒ h/l = 4/5 
⇒ h²/l² = 16/25
⇒l² = (25/16)h²
⇒ h² + r² = (25/16)h²
⇒ r² = (9/16)h²
⇒ (r/h)² = (3/4)²
⇒ r/h = 3/4 

hence ratio of radius to height is 3:4

Answer 2

hey
__________

given
__________

radius of cone = radius of cylinder
height of cone = height of cylinder

CSA of cylinder
______________ = 8/5

CSA of cone

2πrh
______ = 8/5

πrl

2πrh
_______ = 8/5

πr√r^2+h^2

•squaring both sides

(2h)^2
_____ =( 8)^2/5^2
(√r^2+h^2)^2

now see the attachment

hope helped
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