Question

The ratio of volumes of two
cones is 4:5 and ratio of the
radit of their bases is 2:3. find
the ratio of their vertical heights.​

Answer 1

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

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