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Ram and Shyam were given cube A and cube...

Ram and Shyam were given cube A and cube B both having same mass, respectively. The side of cube A is three times that of the cube B. Ram and Shyam found the densities of A and B. What is the ratio of densities of A and B?

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Volume of a cube of length .l. .V.= `l^3`
Length of cube `l_(A)=3l_(B)`
Volume of cube, `A, .V_(A). l^3 A=(3l_(B))^3`
Volume of cube B, `V_(B)=l_(B)^3`
`"Density "=("mass")/("volume")`
`("Density of A")/("Density of B")=(l^3)/((3l)^3)=1/(27)`
Ratio of density =1 : 27.
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