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 $162$ $162$ killograms. [Ans]

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

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

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

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

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

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

The mass of smaller prism is $48$ $48$ killograms.

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