Question

the ratii of the volume of two cone is 4:5 and the ratio of their radii is 2:3 then the ratio of their vertical heights is

Answer 1

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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Hope this will help you...

Answer 2

Solution :-

Ratio of volume of two cones = 4 : 5

⇒ V1/V2 = 4/5

Ratio of radii of the two cones = 2 : 3

⇒ r1/r2 = 2/3

Volume of the cone = 1/3πr²h

Let the heights of the two cones be h1 and h2 respectively.

⇒ 4/5 = 1/3πr1²h1/1/3πr2²h2

⇒ 4/5 = r1²h1/r2²h2 

Given r1 : r2 = 2 : 3

So, 4/5 = 2²*h1/3²*h2

⇒ 4/5 = 4h1/9h2 

⇒ h1/h2 = (4/5)*(4/9)

⇒ h1/h2 = (4*9) : (5*4)

⇒ h1/ h2 = 36/20

⇒ h1/h2 = 9/5

⇒ h1 : h2 = 9 : 5

The ratio of their vertical heights is 9 : 5

Answer.