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Question
The volumes of the two spheres are in the ratio 64 : 27. Find the ratio of their surface areas.
Solution
Let the radius of two spheres be r1 and r2.
Given, the ratio of the volume of two spheres = 64 : 27
i.e., `V_1/V_2 = 64/27`
⇒ `(4/3 pir_1^3)/(4/3 pir_2^3) = 64/27`
⇒ `(r_1/r_2)^3 = (4/3)^3` ...`[∵ "Volume of sphere" = 4/3 pir^3]`
⇒ `r_1/r_2 = 4/3`
Let the surface areas of the two spheres be S1 and S2.
∴ `S_1/S_2 = (4pir_1^2)/(4pir_2^2) = (r_1/r_2)^2`
⇒ `S_1 : S_2 = (4/3)^2 = 16/9`
⇒ S1 : S2 = 16 : 9
Hence, the ratio of their surface areas is 16 : 9.
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