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प्रश्न
The volumes of two spheres are in the ratio 64 : 27. The ratio of their surface areas is
पर्याय
1 : 2
2 : 3
9 : 16
16 : 9
उत्तर
Ist sphere
`V_1 = 4/3 pir_1^2`…… (i)
IInd sphere
`V_2 = 4/3 pir_2^3`…… (ii)
Divide (i) by (ii) we get,
`V_1/V_2 = (4/3pi r_1^3)/(4/3pi r_2^3)`
`64/27 = (r_1/r_2)^3`
`r_1/r_2 = sqrt(64/27)`
`r_1/r_2 = 4/3`
Now, the ratio of their C.S.A
`S_1/S_2 = (4pir_1^2)/(4pir_2^2)= (r_1/r_2)^2`
`S_1/S_2 = (4/3)^2 = 16/9`
Hence, `S_1 :S_2 = 16 :9`
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