The ratio of volume of two cones is4: 5 and the ratio of the radii of

1.	The ratio of volume of two cones is4: 5 and the ratio of the radii of theirbase is 2: 3 then ratio of their verticalheights is
Answer» Let the radius be r1: r2 =2x: 3x V1: V2= 4x:5x Height be h1 & h2 [ Vol . Of cone=( ⅓)π r²h] 1/3π r1²h1: 1/3πr2²h2= 4x:5x r1²h1:r2²h2=4x:5x r1²h1/ r2²h2=4x:5x [ r1: r2=2x:3x] ( 2x²)h1/(3x²)h2 =4x:5x 4h1/9h2=4:5 V1/V2 4h1/9h2= 4/5 h1/h2= (⅘) × 9/4 h1/h2= 9/5 h1:h2= 9/5 Hence, the ratio of heights of the two cones are(h1:h2)= 9:5

The ratio of volume of two cones is4: 5 and the ratio of the radii of theirbase is 2: 3 then ratio of their verticalheights is

Answer»

Let the radius be r1: r2 =2x: 3x

V1: V2= 4x:5x

Height be h1 & h2

[ Vol . Of cone=( ⅓)π r²h]

1/3π r1²h1: 1/3πr2²h2= 4x:5x

r1²h1:r2²h2=4x:5x

r1²h1/ r2²h2=4x:5x

[ r1: r2=2x:3x]

( 2x²)h1/(3x²)h2 =4x:5x

4h1/9h2=4:5

V1/V2

4h1/9h2= 4/5

h1/h2= (⅘) × 9/4

h1/h2= 9/5

h1:h2= 9/5

Hence, the ratio of heights of the two cones are(h1:h2)= 9:5