If the heights of two right circular cones are in the ratio 1 : 2 and the perimeters of their bases are in the ratio 3 : 4, what is the ratio of their volumes?
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40
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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