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प्रश्न
The volumes of two cubes are in the ratio 8 : 27. Find the ratio of their surface areas.
उत्तर
Let the edges of cubes be a and b.
As,
`"Volume of the first cube"/"Volume of the second cybe" = 8/27`
`=> a^3/b^3 = 8/27`
`=> a/b = root(3)(8/27)`
`=>a/b = 2/3` .................(i)
Now,
The ratio of the surface areas of the cubes `= "Surface area of the first cube"/"Surface area of the second cube"`
`= "6a"^2/"6b"^2`
`=("a"/"b")^2`
`=(2/3)^2` [Using (i)]
`=4/9`
So, the ratio of the surface areas of the given cubes is 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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