Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volume is
A. 4 : 1
B. 1 : 3
C. 3 : 1
D. 2 : 5
Answers
Given : Ratio of diameters of two cylindrical jars = 3 : 1
So, Ratio of radii of two cylindrical jars = r1 : r2 = 3 :1
Ratio of heights of two cylindrical jars = h1 : h2 = 1: 3
So, ratio of their volumes, V1 : V2 = π(r1)²h1 : π(r2)²h²
V1 : V2 = (r1)²h1 : (r2)²h2
V1 / V2 = (r1/r2)² / h2/h1
V1 / V2 = (3/1)² /( 3/1)
V1 / V2 = (9/1) × 1/3
V1 / V2 = 3/1
V1 : V2 = 3 : 1
Hence, the ratio of their volume is 3 : 1.
Option (C) 3 : 1 is correct.
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Answer:
Step-by-step explanation:
V1 : V2 = (r1)²h1 : (r2)²h2
V1 / V2 = (r1/r2)² / h2/h1
V1 / V2 = (3/1)² /( 3/1)
V1 / V2 = (9/1) × 1/3
V1 / V2 = 3/1
V1 : V2 = 3 : 1