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प्रश्न
The ratio between the volume of two spheres is 8 : 27. What is the ratio between their surface areas?
पर्याय
2 : 3
4 : 5
5 : 6
4 : 9
उत्तर
4 : 9
Let the radii of the spheres be R and r, respectively.
Then, ratio of their volumes `= (4/3pi"R"^3)/(4/3pi"r"^3)`
Therefore,
`(4/3pi"R"^3)/(4/3pi"r"^3) = 8/27`
`=> R^3/"r"^3 = 8/27`
`=> ("R"/"r")^3 = (2/3)^3`
`=> R/r = 2/3`
Hence, the ratio between their surfcae areas `=(4pi"R"^2)/(4pi"r"^2)`
`= "R"^2/"r"^2`
`=(2/3)^2`
`= 4/9`
= 4 : 9
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Assertion (A)
If the volumes of two spheres are in the ratio 27 : 8, then their surface areas are in the ratio 3 : 2.
Reason (R)
Volume of a sphere `=4/3pi"R"^3`
Surface area of a sphere = 4πR2
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