A right circular cylinder and a cone have equal bases and equal height

1.	A right circular cylinder and a cone have equal bases and equal heights. If their curvedsurface areas are in the ratio 8:5, show that the ratio between radius of their bases totheir height is 3:4
Answer» Let r be the radii of bases of cylinder and cone and h be the height Slant height of cone = √(r2 + h2) ∴ 2πrh / πr√(r2 + h2) = 8/5 h / √(r2 + h2) = 4/5 h2 / (r2 + h2) = 16/25 ⇒ 25h2 = 16r2 + 16h2 ⇒ 9h2 = 16r2 ⇒ r2/h2 = 9/16 r/h = 3/4 Therefore the ratio between radius of their bases to their height is 3:4

A right circular cylinder and a cone have equal bases and equal heights. If their curvedsurface areas are in the ratio 8:5, show that the ratio between radius of their bases totheir height is 3:4

Answer»

Let r be the radii of bases of cylinder and cone and h be the height

Slant height of cone = √(r2 + h2)

∴ 2πrh / πr√(r2 + h2) = 8/5

h / √(r2 + h2) = 4/5

h2 / (r2 + h2) = 16/25

⇒ 25h2 = 16r2 + 16h2

⇒ 9h2 = 16r2

⇒ r2/h2 = 9/16

r/h = 3/4

Therefore the ratio between radius of their bases to their height is 3:4