Question

Diameters of two cylinder are in the ratio of 2:3 find the ratio of their heights if their volume are same.

Answer 1

let the ratios be 2x and 3x
r=d/2
r1=2x/2=x    (h1)
r2=3x/2        (h2)
22/7*x*x*h1  = 22/7*3x/2 * 3x/2 *h2 
h1=3x/2*3x/2*1/x*1/x*h2
h1=3/2*3/2*h2
h1=9/4h2
4h1=9h2
so 4:9 is the required ratio

Answer 2

Diameters of two cylinders are in the ratio 2:3
⇒ r1 = 2x
    r2 = 3x
Given that volumes are also equal
⇒ π(r1²)h1 = π(r2²)h2
⇒    (2x)² h1 = (3x)²h2
⇒     4x² h1 = 9x² h2
⇒     h1/h2 = 9x²/4x²
⇒     h1/h2 = 9/4
∴The ratio of the heights = 9:4