Question

The curve surface area of a cylinder in the ratio 2:3. find the ratio of their height if there volume are same .​

Answer 1

Answer:

ratio of heights = 4:9

Step-by-step explanation:

ratio of curved surface area of cylinders is 2:3

let curved surface area of cylinder A = 2πrh

curved surface area of cylinder B =  2π$lh$

so ( 2πrh) / (2π$lh$)  = 2 / 3

3 rh = 2 $lh$ ⇒ eq 1

given that volumes of two cylinders A and B are same

so πr²h = π$l^2h$

h = ($l^2h$) / r²;

3r [($l^2h$) / r²] = 2 $lh$

3 $l/r = 2$

$l/r = 2/3$

from eq 1 we get $l/r =$ $3/2$ (h$/h)$

⇒  (h$/h)$ = 4/9

ratio of heights = 4:9