Question

two cylinder gas has same volume is a diameter are in the ratio 3:4 find the ratio of the corresponding heights

Answer 1

Let r and R are the radius of base of two cylindrical jars.

Let h and H are the heights of the two cylindrical jars.

Now, 

Diameter of the first jar/Diameter of the second jar = 3/4

=> 2πr/2πR = 3/4

=> r/R= 3/4

Again, 

      Volume of the first jar/Volume of the second jar = 1 {since same amount of the milk contain}

=> πr2 h/πR2 H = 1

=> r2 h/R2 H = 1

=> (r2 /R2 )*(h/H) = 1

=> (3/4)2 * (h/H) = 1

=> (9/16) * (h/H) = 1

=> h/H = 16/9

=> h : H = 16 : 9

Answer 2

Let radii be 3k and 4k

We are given Л(3k)^2h1/Л(4k)^2h2 = 1
                    so, 9k^2*h1/16k^2*h2=1
                so, h1/h2 = 16/9 

So, Ratio of heights = 16:9