Question

a right circular cylinder and a cone have equal bases and equal Heights. if the curved surface areas are in the ratio 8 : 5, show that the ratio between radius of their basesto their height is 3:4.

Answer 1

Answer:

Proved as explained below

Step-by-step explanation:

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

surface area of cylinder : 2πrh

surface area of cone : πr(h²+r²)

Ratio = surface area of cylinder/surface area of cone = 2πrh/πr(h²+r²) = 8/5

⇒ h/(h²+r²)= 4/5 

⇒ h²= (h²+r²) 16/25

⇒ 25h²= 16h²+16r²

⇒ 9h² = 16r²

⇒ r²/h² = 9/16

⇒ (r/h)² = (3/4)²

⇒ r/h = 3/4 

Therefore, ratio of radius to height is 3:4