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Answer (Detailed Solution Below) Option 4 : 16 : 9
30 Qs. 30 Marks 30 Mins
Given: The ratio of the volume of the two spheres = 64 : 27 Formula used: The volume of the sphere = (4/3) × π × R3 The surface area of the sphere = 4 × π × R2 Where R = The radius of the sphere Calculation: Let us assume the ratio of the surface area of the sphere be X : Y and the radius of the spheres be R1 and R2 respectively ⇒ The volume of the first sphere = [(4/3) × π × R13] ----(1) ⇒ The volume of the second cylinder = [(4/3) × π × R23] ----(2) ⇒ According to the question equation (1) ÷ (2) = 64 : 27 ⇒ (R1/R2)3 = 64/27 ⇒ R1/R2 = ∛(64/27) ⇒ R1/R2 = 4/3 ⇒ Let us assume the radius of the first sphere = 4x and the second sphere = 3x ⇒ The surface area of the first sphere = 4 × π × (4x)2 = 64πx2 ----(3) ⇒ The surface area of the second sphere = 4 × π × (3x)2 = 36πx2 ----(4) ⇒ The ratio of the surface of the spheres = (64πx2)/(36πx2) ⇒ The ratio of the surface area of the spheres = 16/9 ⇒ The ratio of their surface area X : Y = 16 : 9 ∴ The required result will be 16 : 9. India’s #1 Learning Platform Start Complete Exam Preparation
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