If the ratio of the volumes of two solid spheres is 27 : 8, then the ratio of their curved surface area is
(a) 1 : 2
(b) 9 : 4
(c) 1 : 8
(d) 1 : 16
WBBSE
Class X
Mathematics
Sphere
01 Mark
2023
(b) 9 : 4
Explanation
Given ratio of volumes = 27 : 8
or, 4\over 3πr1³ : 4\over 3πr2³ = 27 : 8
or, r1³ : r2³ = 27 : 8
or, r1 : r2 = 3 : 2
Ratio of volumes = 4πr1² : 4πr2²
= r1² : r2²
= 3² : 2² = 9 : 4
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