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प्रश्न
The volumes of two cubes are in the ratio 1 : 27. The ratio of their surface area is
विकल्प
1 : 3
1 : 8
1 : 9
1 : 18
उत्तर
1 : 9
Let the edges of the two cubes be a and b.
Then, ratio of their volumes ``
Therefore,
`"a"^1 /("b"^3) =1/27 `
`=> (a/b)^3 = (1/3)^3`
`=>"a"/"b"' = 1/3`
The ratio of their surface areas `=(6"a"^2)/(6"b"^2) `
Therefore,
`(6"a"^2)/(6b^2) = "a2"/"b2"`
`= 1/9 ["since " "a"/"b" = 1/5]`
`=1 : 9`
Hence, the ratio of their surface areas is 1:9.
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