If the ratio of volumes of two spheres is 1: 8, then the ratio of their surface areas is
A. 1 : 2
B. 1 : 4
C. 1 : 8
D. 1 : 16
Answers
Given : Ratio of volumes of two spheres , V1 : V2 = 1: 8
Volume of sphere = 4/3 πr³
V1 : V2 = 4/3 πr1³ : 4/3 πr2³
V1 : V2 = r1³ : r2³
V1 : V2 = r1³ : r2³
V1 / V2 = r1³ / r2³
⅛ = (r1/r2)³
³√1/8 = r1/r2
½ = r1/r2 ………(1)
Surface area of sphere = 4πr²
Ratio of surface areas, A1 : A2 = 4πr1² : 4πr2²
A1 : A2 = r1² : r2²
A1 / A2 = (r1 / r2)²
A1 : A2 = (½)²
[From eq 1]
A1 : A2 = 1 : 4
Hence, Ratio of their surface area is 1 : 4.
Option (B) 1 : 4 is correct.
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Given V1 : V2 = 1: 8
Volume of sphere = 4/3 πr³
V1 : V2 = 4/3 πr1³ : 4/3 πr2³
V1 : V2 = r1³ : r2³
V1 : V2 = r1³ : r2³
V1 / V2 = r1³ / r2³
⅛ = (r1/r2)³
³√1/8 = r1/r2
½ = r1/r2 ………(1)
Now,
Surface area of sphere = 4πr²
Ratio of surface areas, A1 : A2 = 4πr1² : 4πr2²
A1 : A2 = r1² : r2²
A1 / A2 = (r1 / r2)²
A1 : A2 = (½)² [From eq 1]
A1 : A2 = 1 : 4