Question

The ratio of the height of two right circular cone is 1.2 and ratio of radius is 3:4 then find ratio of their volumes
(a) 9:10 (b) 31:32 (C) 9:32
(d) 31:10​

Answer 1

Answer:

The ratio of their volumes is  9 : 32  

Step-by-step explanation:

SOLUTION :  

Let h1 and h2 are the heights of two circular cones and  r1 &  r2 be the radius of the bases of circular cones.

Given :  

Ratio of heights of two circular cones = h1 : h2 = 1 : 2

h1/h2 = 1/2

Ratio of perimeters of two circular cones =  

2πr1 : 2πr2

= 3 : 4  

r1 : r2 = 3 : 4

r1 / r2 = 3/4  

Ratio of volume of two cones =  V1 : V2 =  ⅓ πr1² h1 : ⅓πr2²h2

V1 : V2 = r1²h1 : r2²h2

V1/V2 = r1²h1 /  r2²h2

V1/ V2= (r1/r2)²  × (h1/ h2)

V1/V2 = ( 3/4)² × (1 / 2 )

V1/V2 = 9/16 × 1/2  

V1/V2 = 9/32

V1 : V2 = 9 : 32

Hence, the ratio of their volumes is  9 : 32  

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