Question

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio of 5:3.Then the ratio of their volumes is ..........

Answer 1

Let the ratio of radii of two cylinders = r:R = 2:3

r/R = 2/3 ----(1)

ratio of their height = h:H = 5:3

h/H = 5/3----(2)

ratio of their volumes = v/V = (pi* r²*h)/ (pi*R²* H)
  
= (r/R)²*(h/H)
=(2/3)²* (5/3)   [from (1) and (2)]

= 4/9 * 5/3
= 20/27
= 20:27

Answer 2

let the ratio of radii = x
radius of 1st cylinder =2x
radius of 2nd cylinder = 3x
let the ratio of height =y
height of 1st cylinder =5y
height of 2nd cylinder=3y
volume of 1st cylinder =pi ×( 2x)^2 ×5y
=pi × 20x^2y
volume of 2nd cylinder = pi ×(3x)^2×3y
= pi × 27x^2y
ratio = volume of 1st / volume of 2nd
= pi× 20x^2t/pi×27x^2y
= 20/27 ans. ......