The ratio between the areas of two similar prisms is 4:9. If the mass of the smaller prism is 48 kilograms, what is the mass of the larger prism?

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Answer 1 · 2017-07-29T10:54:47

The mass of larger prism is $162$ killograms. [Ans]

Mass is related to volume , Mass = Volume multiplied by density.

The ratio of area (2 dimension) of two similar prisms is $4:9$

So the ratio of l/b/h (1 dimension) of two similar prisms is

$sqrt(4): sqrt (9) or 2:3$ and the ratio of volume (3 dimension) of

the similar prisms is $2^3:3^3 or 8:27$

Hence the ratio of masses of the similar prisms is $8:27$ .

The mass of smaller prism is $48$ killograms.

Therefore the mass of larger prism is $27/8*48= 162$ killograms. [Ans]